rs tà t r r tt 3 t t s t r t r r tr s r t r t st ss s r

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1 rs tà t r P t 3 s r tt 3 t t s t r rs r str str s 3 3 t r r tr s r t t t2 t r r t st ss s r t r Pr s r s r r t P s tr

2 t r st t s s s r r st s tt è r ù s r t s t r t s r rò

3 t ts tr t r t t s st s q t s r t t s s t r 3 st q t r t t s ts s r t ss str 2s s r s rst s r s P r s r s t st s r s t t t s s tr 2 s s rs r tr s r t s r t r r t rs r2 r s t r t t rs r t r r t r s r t r r t r t t rs s t r r t r r t t s t t s s r s s s r s t s t r ss r r t s2st r2 P r t t s P r r 2 rr r rr rs s s s tr s2st r t r r

4 t r r tr s s r s t r q r ts t r r t r t r s tr s2st r t r t r r r t 3 s2st ss t r t r t t s t t t s s s r ts s ts s r t s s r ts t t r s t tr tr s2st s s st t2 r s r q s r s r rr r r s r q s s r ts t 2 t 1 s t2 t r rr r tt r 2 tt r 2 r tt r 2 Pr ss r r s t r r s ts s s r 2 r 3 t

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6 s st t2 r s r r r t 2 rs t 2 t r t r t t r r t r s s t 3 s2st tr s2st s r t rst r t r 3 t t t r r t r s t r s t t r t t s s t t t s s t t r t r r t r s tr s t2 s r t s s t t s tr 23 r r s t t s s t t s t r t t t t s r t r s s s t r q r s s t t2 t r q 2 t r st s s t t s r r s t s s t t2 t s t r t r t t t r t s st t r r s tr s r t s V/V 1 V/V 2 r t t t r t s st t r r s t tr s r t s V/V 1 V/V 2 t r t t t r t s st t r s r ts t s s t t t t r r t 3 s2st s t t r t r r s t t t t s t t t t t r s r ts t s s s t2 t s t t tr s r s s s t t s t s t r t str t r s t tr s2st r t s2st t 2 t r t s t rr r r t r r t s t r s t t t t t r s r s t t t st t t tr s2st t t t r t t 3 s r ts t s s t t2 t s2st t t t t P t r r t s tr 23 r s t r r t s t tt r 2 r t s t tt r 2 r t s t tt r 2 5 r t s t tt r 2 r t r 2 s tr 23 r 1 s r ts tt r s r ts tt r s r ts r 2 1 s r ts tt r 2 5 2

7 1 s r ts tt r 2 2 str t t t r s r s r tt r 2 str t t t r s r s r tt r 2 str t t t r s r s r r str t t t r s r s r tt r 2 5 str t t t r s r s r tt r 2 s t t r r s t t t r ss r r P > 10 3 mbar s t t r r s t t t r ss r r P < 10 3 mbar r s t t r s t t r sq r s t r r s t st rs

8 st s r r t r t t r q 2 t r t s t t s r s st t s r tr st r r t r s r t s r t r r t rs st r s t rs t t r t r s s t r s r q s t t2 t r t rr r sr t r s r s tt r 2 s r s tt r 2 s r s r s r s tt r 2 5 s r s tt r 2 s r ts t r t tt r 2 t r ss r s r q s t rs s r t r t r

9 tr t r t r2 r t t2 r t 2 rt st r s s t 1 st r t t s s t rt r t r 2 s2 tr r ss s st 2 t s r t s 1tr 2 rt t s t r t s t str 2s ts r t s s t r s t2 s s tr st rs t r t t r t r t t r t s t t rst rs t ts t ts str t r rst r t 1 st r t t r t s 2 2 r s r 2 s r t r t r t s r P t 2 t t t t 2 t r t q t t t 1 t s s t ss r 2 s t r t t ss t st t st 2 rs s t r t t t t s r t r t s ts t s t2 r t 2 rs t r r 2 1 r ts t t r r t s r s t s t r rt s t r t t s t 2 t st t t ts rst s t t t r t t r t s t r s t r r s str t 2 s r t t r r r t t t rs s t s r rt ss t 2 t st s t t rs s t s r t r r t r t r r r t s t t rs r t r r r s t t r t t s t t rs t r t r t t r t s r r 2 s t r r t r t r2 P r t r s t t s t t tr2s s r P s ts r s r 3km t s t r r t t s t s t s r 95km t s s s t t r q 2 r Hz t t t r t t r t t t r t 2 2 r t r 12 t r st r s t r r t r 2 s r s t t r ss r t t t t r r t r s r t r s r ss r t r r mbar t s t r r tr r t r s r s s t s s s t r q 2 s r ts s t s r r s s t s2st s 2 t rs s r tt t r t r t r r s t r s s r r 2 rr r s r s t r r t rt t t t 1 t r t t s t s rr r r ts r s t t t t r r t r s t t s t r s t r s s s st t Hz 1/2 t s r t r t t r t t t r r r t s s t t2 t r r t tt r t t r 2 r rst s t s r s t s r ts t t2 s r t s t s s s s

10 s r s t rr r s t s s t r t t r s r r t t r s t2 ss r s t t t t r s t 267km t r s t r t s r r s t s t s t s rt t r s t s2st s t r t ts t t r s t r r s s t s s t r s s r s st r r ss s 1 t t st rt ts t t s r s r s t r s t s s t t2 r t s rt r t t r s t s t s t r t r ss r s s t r t r t s s t ts t t r r t r s s t r s t r t s r t s rt r r 2 t2 t s r rr rs t r t t t r s t s r r r t s t s t rt r t2 s t t 3 t t r r t r r str 2s s r t rr rs r r t r ss r s t r s r s s t t s r s r t r q 2 r 5 100Hz s t s rt t t r t r r t tt r s s t t2 t s r 1 t t t r s s 2 t q t2 t r t rr rs s t r t t t r 2 st r t r 2 ss t r t r rr rs s s r t t r t r r t r t rs t t t r t s t t s r t t s s t t2 r t ss 2 t rr rs r r s r s 2 t r t r 3 t st s t t t2 t t s s s sts t r 3 t t r r tr t s s t t2 s t s r t t r s rr r s t s s t t2 s s t t s r s ts t r r m t r q 2 5kHz r r t s r t 2 t t r s s t t r t st r s r t t rs t rr r r r r 2 s r t r r r t r s r r r s ts t s r t t t s t t s s t r r t r t 10cm r s s r t 1064nm t s t 2 r r t r t t t t t 1 t t s 2 t t s r r 2 t rr rs s tt 3 tr t t s t tr ts ts r s µm t t r s t rr r t r t r 3 s t r t t s t t t s st t s s t s s t r t t t r t t s t s r tr s2st s t t st t t r r t r s s 2 r t t t r t s t s t s t r t t t s s s t t r t r t r t t s s t t 3 rr t t s t t rr r r r t t t r t t t r r t r s t 1 s s t t2 t s t s t rr r s s s t r r tr t r r t rr t t s t t rr r rr t s s s t t r s r t rr t t s t t r r ts tt t rr r t r r tr s s r s ss s r r t r2 r

11 t rst r t r 3 t t t st rr r t s r r2 t st s t s r r t r q r s s t t2 t s s r s t s str t r r t r rr r s s s t r t r tt t r s rs s t s r t t t t t r s s s str t r s r r r t 3 r2 s t t r ss r t t s r t t r s t ts s s s s r r t r2 s r ts t rs r 2 1 t t r s t rr r s r t 2 t t r t t 1 t 2 t r q 2 r t r st 2 10kHz t rr r s t r r t r t tt r 2 t tt r 2 r s t rr r s t s rs t rt r t s r r s t s t r t 2 s2 tr s t t tt r 2 s t r t r t t s 2 23 r t s t r t tt r 2 t tt r 2 t tt r 2 5 t tt r 2 1 st r t t s t r r t t r2 t r r t t2 s s ss t r r t t t ts t t t 2 t s t s r t ss s r s t s r s r t t r t t 2 t t t t t r s t t t r t r r t r t t r s ss rst t t r r s t s r s s t s r t r r t r t t rs t t t ts t t 2 t r s 2 t t r s t s r s t s r t r r t r t t rs t r q 2 r 5 100Hz t r t r s t t t rst r t r 3 t t t r r tr s s r s r rst t r q r ts t r r t t r s t t r r t r t tr s2st r rt t s r ts t s t t tr s2st t r s s t t2 r r t r 2 t t t s t s r rr r s ts s s r t st ts t s ts r r t r s t s s t t2 rt t r s t t t s r ts t r rr r rst s r t tr s2st t t t t 2 s t s r t t t t r t rr r t 2 t t r s r q 2 2 t s r ts r r rt t r r s 1 t 2 s ss t t s t r r s t t r s ts t t t r t r r t r t t s t

12 t r r t t s r t r2 r t t2 s r t 2 rt st s r r r t täts r t t r s t r2 r t t2 t t r s t r r s t s r r t t s t s r t tr t t r2 s t r t st s q t s r s s t 1 st r t t s s t rt r t s t s t r s r t t s r r t t2 t st s q t s r t t s r r t t st s q t s t s s t t st t t ts s ds 2 = c 2 dt 2 dx 2 dy 2 dz 2 = η αβ dx α dx β, r η αβ s t tr t s r r t t s t r s s t η αβ = s r r t s2st r r r t s r t q t t r r rt t t 2 t r r s s d 2 ξ α dτ 2 = 0 r τ s t r r t s 2 dτ 2 = η αβ dξ α dξ β. t st tr 2 r rt s 2 t s q t d 2 x λ dx µ dx ν dτ 2 +Γλ µν dτ dτ = 0, r Γ λ µν t t r r st s2 s s ( Γ λ µν = xλ 2 ξ α ) ξ α x µ x ν.

13 r t t s t r t s s t r t t r st s2 s r s t t 2 tr g µν Γ λ µν = 1 2 gσλ (g νσ,µ +g µσ,ν g νµ,σ ). r t t t s r R λ βµν = Γλ βν,µ Γλ βµ,ν +Γσ βν Γλ σµ Γ σ βµ Γλ σν s r t s t t s r t r r t s t t s R λ βµν = 0. t s r ts t t 2 r t t t t t s t s r rt s s2 tr2 R αβµν = R µναβ, t s2 tr2 R αβµν = R βαµν = R αβνµ = +R βανµ, 2 t2 R αβµν +R ανβµ +R αµνβ = 0, t t s R αβµν;σ +R αβσµ;ν +R αβνσ;µ = 0. tr t t s t t s r t t s t s r R βν = g αµ R αβµν t r rt r tr t t t s r R = g βν R βν. r t t s tr t t t s t s t t q t ( R µν 1 ) 2 g µνr = 0 ;µ r r t s r Tµν t t t T µν,σ s2 3 s t s r t T µν,σ = Tµν x σ t r s s t t t T µν;σ t t s2 3 s t r t r t s T µν;σ = Tµν x σ Γα σµt αν Γ α σνt αµ r t s r rt s s r t 2 r t r R αβµν g αλ R λ βµν

14 s t t r r ts s st t t s st t s r G µν G µν = R µν 1 2 g µνr. r t s s t tt r s tr2 r 2 t q t s r t t r st q t s G µν = R µν 1 2 g µνr = 8πG c 4 T µν, s t str t tt r t s q t s s s t t t tr t s s t t tr2 s t T µν s t r 2 t t s r s T µν = n s t r rt s p µ np ν n E n δ 3 (x x n (t)) T 00 s t r 2 s t2 t s2st T µν s s2 tr t s r s 2 t ts r t s G µν s r rt t t t st s2 tr t t 2 q t s r r2 t t s 2 t t r s s s r r 1 t t t r ts t 1 st r t s s t t t 1t s t r t t s s t r 3 st q t r r 2 s r t s t r t t tr t s s s tr t r t 1 t t t s t st s q t s s t s 2 r 3 t q t s s r s rt r t r t t s t s r t tr g µν = η µν +h µν, t h µν << 1 r η µν s t t s t s tr s r q t s t s tr r t t r st s2 Γ ρ µν = 1 2 ηρλ (h νλ,µ +h λµ,ν h µν,λ ), t t s r q t R µνρσ = η µλ Γ λ νσ,ρ η µλ Γ λ νρ,σ = 1 2 (h µσ,ρν +h νρ,σµ h µρ,σν h νσ,ρµ ), t t s r R µν = 1 2 ( h σ µ,σν +h σ ) α ν,σµ hµν,α h,µν

15 t s r r t tr t t s r s R = h µν,µν h α,α, h = g µν h µν η µν h µν. 2 r t st q t s ( α α α hµα,ν +hνα,µ hµν,α h,µν η µν h,αβ t t r t t s r αβ h µν = h µν 1 2 η µνh. h β,β ) = 16πG c 4 T µν q t s α hµν,α η µν h αβ α αβ +hµα, ν +h α να, µ = 16πG c 4 T µν. t s 2 s t s q t t s t t s t t t t s r q t t r t3 A α,α = 0 s t tr t t r2 s h µα,α = 0, s q t s α hµν,α = 16πG c 4 T µν. s r t s t2 s T µν = 0 s t q t s t s r r t { α h µν,α = 0 h µα,α = 0 s st s t t s q t s s t r t { ( h µν (x) = R A µν exp ik λ x λ)} r t t A µν t t r k µ st s t s 2 t t s k µ k µ = 0 A µν k µ = 0. rst t s t s t s t t k µ s t r t s st t s t t A µν s rt t k µ s t s t q t r t s t t s t t r q 2 ω k 0 = ( k 2 x +k 2 y +k 2 z )1 2 r r2 s t r t t r s t r r t s tr s r t s t s r t t t s t s q t s t t r t s A µν u ν = 0, t r s t r t 3 r r t t s t r t r 3 r

16 r t st t s r 3 t r t t t r t 3 r u s t r t2 A µ µ = 0. t s st r r t t r h µν s q t s r s t 2 h µν,ν = 0, h µ0 = 0, h µµ = 0. s t s t s tr s rs tr ss t s t t h µν = h µν r q t h µν s s2 tr t s r s t s 2 t ts r rt s r t t t rst r rt2 s str s t s t s t s s t s 2 t r s t st r rt2 s s2st t t r r t t r r s t t t st t s r 3 t t s r r t 3 1 s h µν t s h TT µν = 0 h + h 0 0 h h eik λx λ r h + h r r s t t t st t s r 3 t t s s r ss r t t t r t s s s t r s r s t s r t t ts t r q 2 q t t r q 2 t h s s ss q t t2 t r r s ts t r t t r t t s ts tt r rst t ts t ss r t t st s r t t t s t t r st S µ = x µ A xµ B s q t t s s s D 2 S µ dτ 2 = R µ dx ν dx ρ νρσ dτ dτ Sσ

17 r t r rt t t r t t ss t r 3 t r t r rt t t r t t ss t 1 r 3 t r D dτ s t r t r t t s s r t t t t rt s t r s t t t s t q t s 2 t 2Sµ = 1 2 Sσ 2 t 2hTTµ σ. s t s t s q t t r t s s h + 0 h = 0 S 1 = (1+ 12 h +e ikσxσ ) S 1 (0) S 2 = (1 12 h +e ikσxσ ) S 2 (0), s rt s s r t t r t x 1 s t t r t x 1 rt s s r t t r t x 2 s t t r t x 2 h + = 0 h 0 S 1 = S 1 (0)+ 1 2 h e ikσxσ S 2 (0) S 2 = S 2 (0)+ 1 2 h e ikσxσ S 1 (0) t s s t t rt s s t r t t ( x 1,x 2) t2 s t r rt s t s t s s s r s

18 s r t ss t r2 t ss r t t s s 2 2 t t t r2 ss t r t tr t s r t r t t ss tr t s t r t s tt 2 r t r rt s t tr t s r t tr t d em dvρ q (r)r r ρ q s t r s t2 t t r s t t s r tr t tt r t s E = 1 ) ( d n Rc 2 n, r R s t st r t s r n s t t t r t r t s r t t s r r s 2 t t r t t t r2 ρ s t ss s t2 t s d g dvρ(r)r, r t t t ts t r t rr s s t t t t s2st r t t s r t t t d g = 0 s t r r r t s r t s t r t t 1 s t t t ts r t t q t s µ g = dvρ(r)r v(r) t t s st t r t s r t r t t s s t t t r s r t t r t t s t st t st s r t q r t s I µν dv (x µ x ν 13 ) δ µνr 2 ρ(r) t t t r t t q t q t s h µν = 2G Rc 4ϵν. t s s t t s s r r2 s2st s t st rs ss M r t r t r t r ss t r r q 2 ω q r t s cos 2 ωt 1 I µν = 2Mr0 2 3 cosωtsinωt 0 cosωtsinωt sin 2 ωt ts s r t s cos2ωt sin2ωt 0 Ï µν = 4ω 2 Mr0 2 sin2ωt cos2ωt

19 2 t t t t r t t t st R r t s r h µν = 8G cos2ωt sin2ωt 0 Rc 4ω2 Mr0 2 sin2ωt cos2ωt t t2 s r r2 s2st t tr st rs t r st r M = 1.4M r 0 = 20km ω = 2.5rad/s R = 15Mpc h h µν s t t 1 r q 2 r t t s r t t s r t r s s r t ts r3s r s t r ss t s rt r t t t t 2 t t tr ts r r t 1 r q 2 s f max = c3 4πGM 104 Hz M M. r r t r r q 2 r tt 2 ss t ts tr st rs s str 2s s r s r t t s s r s r t t2 s r t t r t r r rst s r s r 1 s ts st t r r2 s r t r2 s r r s r s ts r t t s t r 2 st t r q 2 t r ss s s rt r t t t s r t tr st rs s rs r2 s2st s st st s r s r ts ss t t r 2 st t t r r s t t t t s r t t t r 2 r r r rst s r s rst s r s t r t ss s rsts t t r2 t r2 rst s r s r rsts r t t t h µν = 0 r t r t rst h µν 0 t r t t t t t r r3s r s s R S = 2GM c 2 t s t r s 2 t ss M s s q t t s t

20 s rsts t r2 h µν = 0 2 r t t t t r t rst t r s r s st t h µν rst r2 P 2s 2 rsts t r2 s r s 2 s r s t r r t t s t r t s s t t 2 rsts t t r2 t t t t rt s t st t t t r2 s t r2 s2st s r s 2 tr st rs r s r t r s r t t r s t ss r t t s t st t t t ts t s2st s r2 s s 2 t s tr st rs r t r q 2 s r2 t 500Hz s r q t r t t t s t r t ss r 2 t r r t t r t t st rs r t r t s r t t t s t t r s s s r s r t st t t t s r s s r 2 s t t r t t r s s t t r s t r t r q 2 s t t r s t st s r t r s r s r r t t s r s t t r s t t t 1 2 t s t s 2 t r r s t s r t t t r s q r st t t r t ss s s s t 1 t 2 t rst s t r s r s s ts r q 2 ts t t t s r t t ssm 1 M 2 r2 s st t r t r q 2 f t st r r t s r r t t r t s t r q 2 s f M 5/3 c f 11/3 + ( ) relativistic corrections t t s r M c s t r ss s A k orbit Mc 5/3 f 2/3 r, M c = (M 1M 2 ) 3/5 (M 1 +M 2 ) 1/5 k orbit s st t t t t s t t t t r t r s t t t s t 2 t t t t t r t t tt s h k orbit M 5/3 c f 2/3 r r s s t r 2 st t t t t r q 2

21 r t r s s t s s t t t r s t r t t s r r s t r2 s2st t r t s t 2 t r t r t tr t2 t r t t

22 t s2st s s 2 t tr st rs t ss M 1 = M 2 = 1.4M r t r q 2 f orbit = 50Hz ( ) 100Mpc h f = 100Hz r t r 2 r t s f r s s t 200Hz s r E M n s n f2 f s t r 2 s 2 t s2st t t r s t s2st s s 2 tr st r ss M 1 = 1.4M ss M 2 = 10M ( ) 100Mpc h f = 100Hz r E M n s. s s r t 1 t t 1 t s t s r t t t r t r s t t s t t t r k orbit t t r t r t s tr t r s r t s r t t t t s t ss 2 t t ss s r r r t r 3 2 t s 2 r s t r s tr rt r r 2 s s str t 615nm 2 t t s t 2 r r t s t rst s s str s 2 s r st r s ts str 2 r s t 2 s r t t r t r s 2 P P st t s r t t 1 s t2 2 st st t r s t t r s t t 2s t r t 1 t t r r s t 2 st t s r r t s r s t s r t2 s t t t t r r r t 2s s s t t r 2 s r r r t r t ss t r st r r2 s2st t s s r s t r ss t t r t ss r s r t t r s 2 r r r st rs t ss M > 8M t t t r t r2 r t 1 s r t t s r tt 2 r 2 r t r 2 tt t s s t ss t 1 s2 tr2 t s 2 t r t t s t s ( ) E 1/2 ( ) 1kHz 1/2 ( ) 10Mpc h M c 2, f r r f s r q 2 r t t t s t r s t st t t s r t s r r E s t r 2 tt t r r t t r t ss r s r s t 1 ss t t t r t t s t r r s t t t t tr r 2 r ss r s t r t r t t ttr t ts s M Ch = 1.4M

23 P r s r s tr st rs s rs tr st rs r st rs t ss s s r t t s r ss t t s r r s s t r s t s 2 r t r2 r t s t s t t s t t 2 r r 2 rt r t2 tr st r r t s r r r s 2 t t s t 2 t tr t r t t r t r q 2 q t t r t t r q 2 2 r t t t r 1 s t t t t r s t s r t r t 1 s s2 tr2 t s s2 tr t r s t s r st r t r t t s t r q 2 t t r t t r q 2 r t ss s s t r s r t t st r s t r st t st t t t t r t t tt s r t t t st r s r t t r r s s r 0.1ms t 1ms t r r t st r ts r 2 E M c 2 r t s t s τ t r q 2 t r t r s s r 300Hz t 3 r 2 t ( ) h E 1/2 ( )( ) 300Hz 1months 1/2 ( ) 15Mpc 10 3 M c 2. f τ r r2 s2st s r r2 r2 s2st s r r t s s t r t t r t t s t r r r t t t t t s tt s s s t t t t t t rt 2 2 t 2 r t s rt r t r r q 2 f 10 3 Hz s r t t ss r t s s r s 2 2 r s r t r 2 rs s r t t r2 s r P 2 t t t r t r 2 s t s 1 t t s s r r 2 ss t r t t s ss t s rt r s t r t r t r t 1 t r t t r2 r t t ss st P = ( 2.403±0.005) t 2s s t s r t t 2 P = ( 2.30±0.22) s s st t t t t r t t st s r s st rt t st st s r r t t r t s t st st r t s t r t t q t t s r r t s r 2 t 2 s t r 2 rs t s r2 t t t t s t s r r t rr t s r s s s t t r t t t s r2 rt t s t s t s r t s t r t s t r s t s s s t st t r2 s tr s t s s r 2 t r t r Ω gw (f) = 1 ρ crit dρ gw dlnf,

24 f 3 t t s r s t 2rs s tr 2 r r t 2rs t s s rs t 10 1 t t t r tr s r t s r t r r t rs s s r t r r t rs rt r2 r s t r t t rs r r s str s r2 st rs s r ss s s r s s r s r r t r t t r q 2 t r t s t t s r s st t s r tr st r r r ρ crit s r t s t2 t rs ρ gw s t r 2 s t2 t st s t r f s t r q 2 t r t r t t t s h f Ω 3/2 gw (f) f, r f s t r q 2 s r t t t t s s s t t r r 2 t s t t t r t t s r t t r r q s t r r s t r 2 t t s t s s tr 2 r t t s t r2 r q s Hz ts t r r t s 3 t rs s t 2 r r t r t t r r s t t r r s t r 2 s t E infl t s ( ) 2 Einfl h rms, r m P s t P ss t t s 2 t s s s s t t r t t s ts s t s tr 2 st t 1 r ts t t s r t s s tr s r r s t t r t s t2 t rs s s m P r H 0 s t st t ρ crit = 3H2 0 8πG,

25 t t rt t s t s t s r t r t r s t r t t s ts s s t t s s st rt t 1 r t r t r r t r t t t s t t s q t 1.4m r t2 t s t r r s t ss r t s t r q s t 3 s s rs t s s r t s r r t t s s s t s r t t r q 2 t tr t r t t r t t s r s r s r t t ts s tr t r t r t t t s t r s t s s t r t t t r q s t r r 10 9 Hz q t t t r 2 t t tr t x 1 s s cdt = dx t r s r t t t s q t cdt = [1+ 12 ] h(t,x) dx. t s t s s r tt t t t 1 t 2 r t cdδt = 1 2 [h(t 1,x) h(t 2,x)]dx, r δt s t t t r s r P t t t λ tr st L t t h(t)p L, L λ δt λ h(t)p, L λ s r s t t t r r t r t t s r tt 2 r2 s2 t r t r t r t t t t t t s s s t δt hτ, r τ s t r t r t r2 s2st s s r t r q r s 1tr 2 r s s t st ts t t t s r rt2 r t s s rs t t s s t t2 r tr s r t r t t s t r q s t Hz t t t r t r tr s r t s t s s t r t t r t t s r t 2 t r t t s sts t s r s r t 2 st st r s t r r t rt t s t t t t s s t s t t rt r s s t r ts r q 2 s r t t t t r s t r q 2 s t δf t t s r t t t r t t t δf f 0 h TT µν.

26 r t2 r t r t t t r t t s r t 2 r2 s2st t r t t s s r t s s r ts r s r t s r ts 2 r P r P r t s 2ss s t s ss t s r s r t s t t t t t s s s r t r r t rs s r t r r t rs r s t t t r t t t r r q s t Hz t r r t rs rr t 2 s s r t t t t 2 r t t r t t s tr s t t r t t t s s t r r t r s r s s 2 s tt r t t s t t t t rt s t t r r t 2 t rr rs s t t t t t r s t s t r t r t s s r t s tt r s t t t s t r t t t r r r t 2 q t s r t 2 t rr r rr t t s tt r t t s s t t 2 r r t t s t t s r t t t t r s t t r r s r t t s 1tr 2 s ts r 1 t t r t L = 10 4 m t r t t t L = hl m. r r r t r t s s r t s r t r r t r t t rs s r r r t r s t t t t s r2 r s 2 r2 P r t t s t r t t t t 1 ts r t t rt r r 2 rr r s t t 1t t r t r s r t t s t t rs t r s s r t r r t r rr t 2 r t r r r st t r s s t r r t s r t r r t r t t r t t st s t r t s t s s r t r r t r t r t t s r t r2 t s r t 2 t s s t t2 t r2 r q s t 0.1mHz 0.1Hz ss t t rt s t s t s s 2 t r s r ts t t rt s q t r tr t s s

27 r s t r r s t t t r t t r r t r r t s t s s t s t 2 t s t r2 P r t t2 r r 2 s t r2 P r t r t s r 2 s r 2 s t r2 P r t r t s

28 s t s t 2 st s rt r s t rst t r 2 t t t r r r s t s r r s r t r q 2 3 s s t t2 t 3 Hz 1 2 t 2 r r 2 r r 2 s t r2 P r t r t s r r 2 s t r2 P r t r t s r 2 s t 2 r t r t r t r 2 s t r2 P r t r t s r t st t s r r r t r t t r s r t s r t r r t rs

29 r r t r t r s r s t r km r t t s s r t t r r s r t s r r t s r 2 t t r t st s 2 r t t ss r s t r t r t t t r2 r s t r t t rs t rst s t t t r t t s s t r s t r r s 2 r s t s s s 2 t ss tt t s r s r s r s r t s r st t k t r t l 0 r t r t t s r t x 1 s r t t tr z 1 s t q t t s m d2 ξ dt 2 +mω 0 dξ Q dt +mω2 0ξ = 1 2 ml 2 h + 0 t 2, r ξ s t s r t m s t ss t t s Q s q t2 t r t s t t ss t t s2st t t t t t 1t t r ω 0 s t r r s t r q 2 t s s t r s 2k ω 0 m. q t rr s s t t t r s t r s 2 r t t s t r t t s r 2 t r t s t r s

30 s t P r t3 r r t r 3 r s t t 2 r t r 3 r t 2 rs t2 st r str str s t t rs t2 t r ss t r q 2 3 t r t r s s t t2 Hz st r s t rs t t r t r s r s t r st r r t s r s r s t t s r t t t r t t ss 2 rs t r s r r s t r rt t r s s r ts s t s 2 t t r s t rs t r st t t 1000km t r t r t r2 t t rs t2 r2 s r t s r r t t t t r s st r t t s t t r r 2 1 r ts t r s t rs t 2 t t r st r t st t t t r t r s t

31 t r r t r r t r s r t r r t r t t rs s t r r t r st 1 r 2 t s t r r t r r t r s t r t s t t t s s r t r r t s r r s t s t s t r r t r t t r s s t t t s r q 2 f r k t r t s t x 1 s ts tr s E in = E 0 e i(2πft kx). s r s tt r t r t t r BS = 1/ 2 tr s ss t t BS = i/ 2 t s tt tr s r E t = i 2 E 0 e i(2πft klx) E r = 1 2 E 0 e i(2πft kly), r L x L y r t t t t r s t r t s t t t r s t s r r t 2 t rr r t s r 1 = 1 r 2 = 1 s t tr s r t s r t r t r t t t s t t s tt r t 2 r r s t 1 t tr s E out = t BS r 2 E r +r BS r 1 E t = i 2 ( 1 2 E 0 e i(2πft 2kLy) ) ( i 2 E 0 e i(2πft 2kLx) ) = i 2 E 0e i2πft( e i2klx +e i2kly ). r t t s q t r s r 2 t 2 2 e k L t L = L x L y t E out = ie 0 e 2ikLx e i(2πft k L) cos(k L). st t t t t t s t t s tt r t 2 r r t t t t t t s r

32 r s t r r s t t s t r r t r ts tr t t t s r ss s t E back = ie 0 e 2ikLx e i(2πft k L) sin(k L). r s t rs t t 1 t s r P out = E out 2 = P in cos 2 (k L) s P back = E back 2 = P in sin 2 (k L) P out +P back = P in ( cos 2 (k L)+sin 2 (k L) ) = P in s 1 t s t r 2 s r t q t s t s t t t r t s 1 t r t x y r t s t r t t t r s t s t r t t s s t t r s t t s φ = 2k L. r r t t t t 1tr s s r str t t r r { Pout = P in, φ = 2nπ P back = 0; str t t r r φ = (2n+1)π { Pout = 0, P back = P in.

33 t n N t q t t2 out Pout min Pout max +Pout min, C = Pmax tr st t t r r t r t q t s q t s P out = P in 2 C = 2r 1r 2 r1 2, +r2 2 (1+Ccos φ). t tr st t s t r r 2 ss s t rr rs t s s2 t r q t t t r s2st t s C = 1 r t t s t t s t r t ts r t t s t t r r t r s r s rst s r t r t x 1 s r t ds 2 = g µν dx µ dx ν = (η µν +h µν )dx µ dx ν = c 2 dt 2 +(1+h 11 (2πft k x))dx 2. r t s q t t r t t τ out t 2 t t tr t r r t s tt r t rr r s τout 0 dt = 1 c 1 c L 0 L 0 1+h11 dx ( 1+ 1 ) 2 h 11(2πft k x) dx, r s r st t t r t r t 1 s h 11 τ out = L c + 1 2c L 0 h 11 (2πft k x)dx. t t τ rt t 2 t t t r t rr r t t s tt r r τrt τ out dt = 1 c 1 c 0 L 0 L 1+h11 dx ( 1+ 1 ) 2 h 11(2πft k x) dx, t t 2 s τ rt τ out = L c 1 0 h 11 (2πft k x)dx. 2c L t t t t t 2 t t t t x r s τ rt = 2L L c + h 11 (2πft k x)dx 1 0 h 11 (2πft k x)dx. 0 2c L

34 t t t t t r s r t s t s x t t r tr t s t = x c t r tr t s t = L x c r t t q t s 2 τ rtx 2L c + 1 2c L 0 h 11 ( 2πf x c k x ) dx 1 2c 0 L ( h 11 2πf L x ) k x dx. c t t s t t t t t 2 t t t t r t y 1 s τ rty 2L c + L 0 h 22 ( 2πf y c k x ) dx 1 2c 0 L ( h 22 2πf L y ) k x dx. c s r r t t r t s t z 1 s t r 3 t r q 2 f gw t q s t r t t r s h 11 (t) = h 22 (t) = h(t) h(t) = he i2πfgwt, q t s τ rtx 2L c + τ rty 2L c h ( ) e i2πfgwl/c 1 i2πf gw h ( ) e i2πfgwl/c 1 i2πf gw t tt r t t t r t tr t t t t r s s τ = 2L ( L c heiπfgw c sinc 2πf L ) c t r s s t s φ = 4πL ( L λ heiπfgw c sinc 2πf L c ). r t r t t t r s t t r r t r r t s s st t2 t t t r t t 1 t tr φ(f) s s r s s t t t r t t rt r t s r 1 t 2 st t r t tr t t t s 2πf gw τ rt 1 t s x s r s s s s x = sinx x

35 r r t s r r s t t t r q 2 r t r r t r t λ = 1064nm L = 3km t r t tr t t t t r s r 1 t t τ (t) = 2L c h(t) t r s s t s φ(t) = 4πL λ h(t) s s r s s s t st t r t2 r t t s r2 s t s t t t t t r s r2 s t st t r t s r s s s r t r r t r t t r t t s t t s s t r s s s s tr t s r r t t t r r q 2 f < 5Hz r t r s s s r r q 2 5Hz < f < 100Hz r t r t r s r r q 2 f > 100Hz r t r s t s s t t s s tr t s s s s s s 2 r s t t t t r s s s r 2 t s r s t r q 2 r 1 r t s r ts t t t s tr t ts t t s s s t s x(f) f 2 m Hz.

36 r s t t2 r tr t s s r t t t r r t r t r t q t L rr s s t t t r t t h seism (f) = 2 2 L x(f). s t 1t s t t s s s r r t r t s r tt t r r s t r s s t t r t r s rt s s s t s r s r r q s t 5Hz 100Hz r s r t r r t r t t rs r t r t s s r 2 rt r t 2 st 1 t t t s sts r t rt s r s t t r t r F frict = ηẋ t η t t s s t2 st rst t t t s r t s t t s s t rt s t t t t t t t s t t t ss t t t r 2 st t t s s t s x 2 th = k BT 1 3πaη τ, r a s t r s t rt s τ s t r t s r t s r s t s r2 rt t s t r t rst t t t t t t ss t

37 s r ss s s s s t ts t t rt s s s t r 1 r t r t ss m r ss s t r A s s t r r t r s r q 2 f 0 s t t r t r T r s t2 rt s n r ss r p = nk B T k B s t t3 st t r t t s r s t s F = pa = nk B TA t r t s s s N = 1 4 nva = na k B T 2πµ, r v s t t2 t rt s s µ s t ss t s 2 t t t r ss 2 t P ss st t st s s rt s rr t rr t s t t t t t t r rt s t t s t t t s σ Nτ = Nτ r t t t t r t t s σ 2 F = 4(k B T) 2 na vτ, rr s s t r s tr s t2 t r 2 r t t r t r s F 2 (f) = 4(k B T) 2 na v. F frict = ηv p = 1 4 navv p, r v p s t t2 t t t s r t s t r t r ss t F 2 th = 4k BTη. t t ss t t r t t ss t t r s t r t s t t r s ss t s2st t r 2 q r r 1 t t r t s s t t t s t Z(ω) t tt Y (ω) Z F ext v Y Z 1 t t q rt t t r 1 2 mv2 = 3 2 kbt

38 r F ext (ω) s t r t r s s t2 t v(ω) t s2st t t ss t t r st t s t t t r s tr t t t r s2st s 2 F 2 th (ω) = 4k BTR(Z(ω)) r t r t s2st s t t t x 2 (ω) = 4k BT ω 2 R(Y (ω)). s t r s r2 s s t s t t t t t t t t t t t r s 2s s t s2st s s str t r s 1 s t t t s t r t tt r rst ts t t2 s r t s s t r t r r rt t t2 s s t st t r t r str t r r t rst s s r s s ss t s s r F vis = ηẋ t q t t s mẍ+ηẋ+kx = F. s q t s s2 t s s t r r tr s r s 2 mω 2 x+iωη x+k x = F t tt Z(ω) = η +iωm k iω Y (ω) = 1 η +iωm k iω = η iω + ik ω η 2 + ( ωm k ) 2. ω t s tr s t2 t s t s t s x 2 th (ω) = 4k B Tη (k mω 2 ) 2 +η 2 ω2. r t s r t r s r q 2 s k ω 0 = m t t r t s q t s s 2 t t x 2 th (ω) = 4k BT mq Q = ω 0m η ω 0 ( ω 2 ω 2 0) 2 +ω 2 ω 2 0 /Q2

39 r ω ω 0 x 2 th (ω) = 4k bt mqω 3 0 = constant, r ω ω 0 x 2 th (ω) = 4k btq 1 mω 0 ω 2 1 ω 2, r ω ω 0 x 2 th (ω) = 4k bt ω 0 mq ω 4 1 ω 4. str t r t t r s r t r 3 r t r r t r 3 2 ss φ(ω) F fric = k[1+iφ(ω)]x(t), t q t t s t s mẍ(t)+k[1+iφ(ω)]x(t) = F (t). s t s r ss s r s r t t r t str t r t t r s Q = 1 φ(ω 0 ), t r s tr s t2 t t s s 2 t t x 2 th (ω) = 4k BT ω0 2 ( mqω ω 2 ω0) 2 2 +ω 4 0 /Q 2 r ω ω 0 x 2 th = 4k BT 1 mqω0 2 ω 1 ω, r ω ω 0 x 2 th = 4k BTQ 1 m ω 3 1 ω 3, r ω ω 0 x 2 th = 4k BTω0 2 1 mq ω 5 1 ω 5. r s t 1 s t tr x 2 th (ω) t2 t r t r s s ss s r t t st t s t t r s t t t s s r t ss t s t s2st t t r s r q 2 t s s r 2 st r Q = 2π r 2 st 2 t t t r r q 2 r t s Q = ω 0 ω,

40 r P r s tr s t2 t s t rs t ss m = 1g r s r q 2 ω 0 = 1s 1 Q = 100 s t s s s s t str t r ts t x 1 s r s 1 t y 1 s r cm 2 /Hz r ω s t t r t r s t t 1 s ω st t r 2 s r t r s Q r r r t 2 t s r 1 t s r t t t s t s r r s r ts 2 t ss s s r { F 0 cos(ω 0 t+δ), r t < 0 F (t) = 0, r t > 0 t F 0 δ t r tr r2 st ts t s2st tr t r s t r t q t r t > 0 t s t mẍ+ηẋ+kx = F (t) x(t) = A 0 e t τ sin(ω0 t+φ 0 ), r A 0 φ 0 r t st ts 2 t t τ = η 2m. t t > 0 t t t s t s s t 2 t 1 t A(t) = A 0 e t τ, r τ s t t t A(τ) = A 0 e. 2 t t t t r t s s s Q = ω 0τ 2.

41 1 s t t r 2 t t t t r s s2st s t s 1 s t t s s t ss t t t t t t s r t s t r t s t s2st ss s r s t rs s r 2s q t t2 X s2st s s X(t) = u(r,t) P(r)dV, r u s t s t P s t t t 2s q t t2 s r t s t t t s2st s r r F (t)p(r) t s t s u(r,t) = n w n (r)q n (t), r w n (r) q n (t) r t s t t t r t n t r s t t s2st q t t r t s r s t r ss m n r s t r q 2 ω n m n q n (t)+m n ω 2 nq n (t) = F (t), t ω n t r s t r q 2 t n t s X(t) s t s r s t X(t) = w n (r)q n (t) P(r)dV = q n (t). n n r 1 t s s s r q t t s x 2 th (ω) = 4k BT n ω n 1 m n Q n (ω 2 ωn) 2 2 +ω 2 ωn/q 2 2 n r t str t r q t s x 2 th (ω) = 4k BT ω n 1 m n φ n (ω)ω 2 n (ω 2 ω 2 n) 2 +ω 4 nφ 2 n(ω). t t t t r s st t ss m n t r s t r q 2 ω n t t r r s t t r r t rs t r s t t r r t r t t rs r t tr t s t t r s s t t ss r 2 s 2 t 1 r ss t s φ p (ω) = φ w (ω) E el E el +E grav φ w (ω) E el E grav, r s t t wn(r) P(r)dV = 1, t 2 t t t t w n(r) s t t rt t s2st t st r 3

42 r φ w s t ss t r E el E grav r t r s st r 1 r r t t t s r st t k el = N TEI 2l 2, r N s t r r s T s t t s E s t s I s t t rt t r r ss s t l s t t t r t t s r st t s s k grav = mg, l E el E grav = k el k grav φ p (ω) = φ w (ω)n TEI 2mgl t q t t t r s tr s t2 t t t t r s s t t x p (ω) 1 Nm, s t r s r s t r s ss r r s rt t r s s s q t s r t2 t rt t rt t t rr rs t t r r t r t r t r t r 2α t rt t r 3 t t 2 y 2 (ω) = α 4k BT mω ωvφ 2 v (ω 2 ωv) 2 2, +ωvφ 4 2 v r ω v s t r s t r q 2 rt l r E r t r s s s t N r s t s πen ω v = r. ml s t r s r t t s t s r s t 2 r r t s r s t r q 2 t r s s ω n = nπ mg l πr 2 ρn (1+a), r n s t r s r l r r t t t r s t r s m s t rr r ss 2 t r s ρ s t s t2 t r s a = 2 l πer 4 N 4mg.

43 t r s tr t s x viol = N 4k BT ω 2ρr 2 l 1 πm 2 n 2 t t ss 2 φ n = n ωnφ 2 n (ω 2 ωn) 2 2, +φ 2 nωn 4 aφ(ω n ) 1+ a 4 n2 φ 2 (ω n ), s t r s r t tr t t t r s 2 t r s r q s s r t t t t r s t rr r s r s 2 st t s t t x 2 th (ω) = 8k BT ω U strainφ(ω), r U strain s t str r 2 st r t t ss t t t rr r s r s r r t t s t t s U strain = 1 σ2 2 πyw 0, r σ Y r t P ss r t t s t rr r w 0 s t r s t 2 t s tr s t2 t rr r t r s x 2 th (ω) = 8k BT ω 1 σ 2 2 πyw 0 φ(ω) t ss t r s t ss s φ(ω) = φ mat (ω)+ [ ] U i (ω) φ i, U i strain r φ mat s t ss t t r t rr r s φ i U i r t ss t r 2 t i t ss t s r ss t s s t s s r t s t s t t t t t t s t t r t t r t rr t s t s r ts t r τ s N = nτ r n s t t s r t s t 2 rr s r t t 2 t r t2 str t s t P ss str t P (N) = NN e N N!. N 1 t r 1 t t ss str t t st r t σ N = N. t r t r s s r t t t rr r t s t s σ N N = nτ nτ = 1 nτ.

44 t t t r t s s t t 2 t t t t r 2 t r t n = λ 2π c P out s r t s s t r r t r r q t δl = λ 2π arccos ( Pout P in ), t s r t P out r q t δl = λ 2π arccos 2π cn. λτp in r q t s t s t r t t σ δl = dδl dn σ N = cλ 4πτP in s δl = hl t t r t t t t σ h = σ δl L = 1 cλ, L 4πτP in rr s s t t s tr s t2 h shot = 1 L λc 2πP in. st t t t s t s r s s t r s t r r t t s ss t str t t t t s t s r t r r t t s t s s r t st t t t t s t r r t r ss r t r ss r s t t t s t t s r t rr rs r 1 rt 2 tr t t r P s F rad = P c t s r r s t t t t t r r t t t s tr s t2 s Pin h rad = 4π2 mω 2 L 2π 3 cλ, r m s t rr r s ss t s s t s r t s t s t s r s s t t r s t r s st t P in t t r s s t t s t 2 r s t t r s st s t s 2 t r t t s s tr r h rad (ω 0 ) = h shot (ω 0 ) P opt = 4π 3 cλmω.

45 r t 2 t r ts t r s r 1 t t 1t r r s s r t r r t r t t 2 r P s t tr2s s t s t 2 r t t t t r t t s rt r r t t s r t r2 r r t s r t t r r t t t t r ts str t s s t 2 t r t s s t r P r2 r s r r 2 s t r r t r t r s 3km r2 P r t r s t t s t t s s s r t s2st t s r t 1064nm r 20W t s r t 2 t s r Nd : YVO 4 t r t s r Nd : YAG t r 1W t s rs r t r st t r t t s t s t r q MHz t r tr t t r t r t s t t s r t rs t rt t s2st t t s t s s t r t r s t t r t2 t t 144m ss F = 1000 s s t r t r t t t r2 P r t t s s r 2 s r s 2 s s t t r s t t t r s t r t s s t t2 t t r r t rs t 1tr 2 t 1t s t r t t t t ss st t s r r s rs tr t s

46 r s t r2 P r t t2 r s r t t tr r r t r s t t t t r t r r t r t t r s r2 P r t t s s st t rr rs t st L = 3km t rr rs st t rt t r r s t 2 r st rt r r rr rs t 2 ss 21.2kg t r 350mm t 100mm r t t2 r i = 0.88 rr rs t t t r s st rt r t s ss s s t t rr rs t t 2 r rr rs t r t r r s R c = 3450m r t t2 r E = 0.99 s r t r t t t s tr s t E 0 t s rt 2 r t rt 2 tr s tt 2 t rr r t r s t t s r 1 E 0 t 1 E 0 tr s tt r rr r t s rt 2 r t rt 2 tr s tt t t s t 1 r 2 E 0 e ikl t 1 t 2 E 0 e ikl t s tr s ss s t t t r t tr s ss t t2 s r c = r 1 +t 2 1r 2 (r 1 r 2 e i2kl) n = r 1 + n=0 t 2 1 r 2 1 r 1 r 2 e i2kl t c = t 1 t 2 e (r ikl 1 r 2 e i2kl) n = n=0 t 1 t 2 e ikl 1 r 1 r 2 e i2kl t 1 1 t r 2kL = 2nπ t s s t t t t2 s s t r s s r t2 t L t t t s L ott = L 2F π,

47 r tr t r tr s ss r t r s t t t s t r t r s r F s ss t s s r t s r ss t r s t2 t s s F = π r 1 r 2 1 r 1 r 2 r r 1 r 2 r t r t ts t rr rs t s r t t2 t t L = 3km ss F = 50 s r s t t L ott 95km P r r 2 rr r s s r s s t t t r r t r s t r r str t t r r t rt t t t 1 t r t t s r t t s r t r t r r t r t s r r 2 rr r P r t r t s r t s2st 6m r t s tt r t t t t s r t t 1 t t s t t t r r t r r 2 rr r r s ss 750g t t r 120mm t ss 30mm r t t2 r r = 0.92 t r r s s t G PR t r t tr s s ts t r 2 rr r r r t r t r t t t t r r t r r int G PR t 2 r (1 r r r int ) 2. t t r s rt t s s t s q t t r s t s t s r r G PR = 50 h shot (f) = 1 ( ) λc f 2 4π , 8LF ηg PR Pin r L = 3km s t t r r t r r t F = 50 s t ss η = 0.93 s f p

48 t t 2 P = 10W s t s r r t r t t s t r2 P r t t r q 2 rr rs s s s f p = c 4LF 500Hz t r q 2 t s r s s t s s s t t rs rr rs r s t r t r s s t t r r t s s s r tt t r s r t r s s s t 10m t r s s s t r q 2 r t r3t t s s 2 rt t t rs t 2 rt rt s s 2 t r rs 10m t t t r t r 1 ts t t t r s t r t r r s s s rs t t s r s t r t t t s ss t r t t r q 2 f0 IP = 1 k 2π m g l, r k s t t st st t m s t s s ss l s t t s r r f IP 0 30mHz t rs t r s tt t t r t rt t s s 2 t rs t t r st 2 rs t r t r st r t t tr r s r s s r t t t t t rs s 9m t s r s r q Hz s t r s r 3 t s t s t r r q s s r s t t r rt t t t r q 2 1.5Hz t rt r r t r t s t s r s t s2st s 2 t ts t 2 rt r t t 2 r r t 2 t r s r s s t t r s s t y t r s r s F y d, r d s t st t t t ts t 2 s r s t t st st t rt 2 t t r q 2 t r s t s r t 0.4Hz P 2 2 s t st st t s s s t s s 2 t r t ss t r tt t rr r s r r tt s s st st tt t t st t r t r t r st r t t r 1.85mm t 1m rr r

49 r t ts r s r tt t r

50 r t t r r s t tr r s r s r st st rr r s s s

51 t r t ss r s s r t r tt t st r 0.3mm 0.6mm t r r s t 2 t t t s r tt t r t r tt t r t ss t r r s t t rs r r t rr t 2 t t rr r r t r s t 1µm t t rs t t t r s t t t s r tt t r t s t r tt t r t ss s st s t 2 rr ts r t t tr s t t t ss 2 t ts tt t t r tt t t rr r tr t r t s r r r t t s t t r2 P r t t r r 2 r s t t t t t r r t s t s t t tr s t t r r t r t r s t t r t t r 2 t2 P t r t st s t t s tt r t t t rr rs l 1 l 2 t t r t t t t r s L 1 +L 2 L 1 L 2 tr t s s t t t t t t r r t tr P t t t t s r s t t t s t r str t t r s s t t 2 t s r t t t rt t t r r t r s r s2st r r t r 2 s r s t r ss r t t r t t r s t ts t t r r t r s r r r t r t s2st r t t rs r t r r t s r tt t rs r t t t t s t t r s t r r ss r t r r 10 7 mbar r H 2 O 10 9 mbar r H mbar r 2 r r s mbar r t t r s t t r t t r t r ss r s 10 6 mbar r t t t t r s s t s t r t s s t t2 r s rst r t s r r ss t r r r r s t r s t r r r s s t t2 r s t 1t s t 1 s t st rt t s t t

52 r s t t2 r s r r t t t t t s s s r t s r t s r 2 t2 t 3 r r2 tr s2st r r s s t t2 t s r s2st r t s s s t rr r t s s s s sts s r s t rr r t s t t s ss t r t t r s r r t t t r s r s r 4W t 17W t t s q t r t t s t s t r s t s2st s tr r r t s t t r ts t t r s t r t t s ss s r r t s t t r s r 95km t 267km r s s t s s t t2 r s s t rst r ss r r t s st r str t t r t r r s r t t r r t r t s t s r r t rs t r s s t t2 t r r t tt r t t r 2 r s r

53 r s st t2 r s r r r t 2 rs t r r t r t r t s r r rt r r 2 t2 t t t r r 2 t r s r 2 t t s tt r t t t r t t s t s s t t2 r t 3 t t t r r str 2s s r t r s ts t s s t t2 t r q 2 r s t r t t s ss t r s t s t ts st t t t r t r2 P r t t s r r t r s t s t r t s r r r 17W t 200W rr r t rr r t s r s t s r t ss 42kg st 20kg s t r t r ss r s r s t t r r r t t rr r t t r s Ta 2 O 5 r t t t Ta 2 O 5 t t r s t q t2 t r t rr rs r r s s r s 2 t r t r 3 t t r r tr s s r t s r t t r t t st ss s r st t t t r r t r

54 r t 2 t r t t t s s s t t 2 s s r st s rr r s s s r tr s2st t ts t z 1 s r s t t t r r st ss s r t rr r s s 2 s s rs r ss r H 2 O t r r s r 10 7 mbar t 10 9 mbar t 2 t r s s r

55 t r t r r tr s s r s t s s t r s t r t s t t tr r s t rr rs t 2 t r r s t t t s r r r t r s t r t r ss r s t r t t r r t r t r s t t r s 1 t t r s t s t t ss t2 t s r t r r t s r r t ss 2 t rr rs t t t s r t t s s t r r tr s s r t s s t t2 t t s r ts t r t rr r t st t 2 s r t t r t rr r r s r 2 s r t r t s 2 r t t s t t 2 t s s r t s t r s r t s r t s r t t t r t r r2 t sts r ts r t r 3 t t r t ss 2 s s r ts t t st rr r r r t s r r ss t r ts s s t t2 r q r ts t r r tr r t t t t rs t r s t r q s t s s rr rs t r t r q 2 r rr r s 1 t t t r s t r q s t rr r s t r t t s r t t t 2 s t t t t r s s r t t t q t2 t rr r r q t t t t r s t r s t rr r t r s r r s t s t r r tr t t r s t s r t s ts t rr r ts t rr r t 1 t t r t r s t r q s r s t r t s t 1 t t r t r s r s r t s r t s r t t t t t q t r rst st t t r r t t 1 t r t t t s r r 1 t r r r s t r q 2 ν 0 5.7kHz t r Q 10 6 t 1 t t r t F N t t s s r t s t q t t t t rr r ts t s A 0 = F 0τ 2ω 0 m = F 0Q 4π 2 ν 2 0 m m.

56 t t t s r ts t s r t t t = 6τ = 300s s s t t2 x = A 0 e t τ m. rr r r s r q s t 2 10kHz s t s s s t t2 t s r t r t st s r s t t r q t t t t s s t t2 t r r t r s dp out dl = 2kP incos(k L)sin(k L) s t s r ts t r s t st ss s s t t2 t t t t r r t r s s t t2 s 1 t k L = π 4 r dp out dl = 2kP in. s s t t t 1 s s t t2 t t r r t r s r t r r P out = P back = P in 2, r s q t r s r ts t r rr r s r r t r t r r t r s s s t r s t r t s r t rr r r r s t s rr r s t r r r s ts t r s s r ts r r t t r t r r t r r 2 t 2 r r st t t r r t r t r rr r rst r t r 3 t t t t t st rr r r r t r 2 ts r r s t r r t r t r s t r r t r s t r s r ts s s t r r t r s r t r t 10cm t t s r t t r2 s r s s t r t t 1 t t s t r r t r s s 2 s r t t 1064nm 1 r 250mW r 3 s tt r t s A = (25.40 ± 0.25) mm r t R = 50%±5% t 3 r s r t 1064nm rr r t t r 12.7mm r t t2 99.5% tt 3 tr 3 s2st t tr s s r t s s 2 t r 3 r t t rs 2 tr t s t r 12µm t s t s t r s s t2 t 1064nm α 0.6A/W

57 r t r t t r r t r r s s t 3 s2st

58 r tr s2st s r t rst r t r 3 t t t r r t r tr s2st rst r t r 3 t t t r r t r s t r tr s2st t s r t t rr ts t t t s r 2 q t s I 1 = αp out I 2 = αp back, r α s t r s s t2 t t s P out P back r 2 q t s s t t r t r st s t ts t tr s2st r t s t r s t rt t t t rr ts t t t s t s t t r r s s t r s t r t t t st t s s s s t r t t t t r t s r t s t t 1 t r t t s r s t t r s P P r t r t s t r s s r rr t t t 1 t r t t ss s t r tr s r r r t rt t t s t s rt r t t t t s s t s s rst st s t r q 2 f 01 = 45.15kHz t t t t s V 1 = R 1 αp in cos 2 (k L). 1+ f2 f01 2 rr t t t 1 t r t t ss s t r rst st 2 q t t t t s V 2 = R 3 αp in sin 2 (k L). 1+ f2 f01 2

59 r s t r s t t r t t s s t t t s t t t t r t t t s s t t t t t s t ss t r rt r st t t r q 2 f 02 = 72.34kHz r r t t s t t 2 t t s s ss t r st t t r q 2 f 0 = 72.34kHz 1 t t r s t t s s 1 V = 1+ f2 f0 2 V 2 1+ f2 f 2 02 V 1, r s r t t R 2 = R 4 = R 6 = R 8 = R 9 = 1kΩ s t s t t t t t r C 4 t s r r r t r t r q 2 t r s q t r t s 1 V (V 2 V 1 ). 1+ f2 f0 2 s rt r st r r t t ss t2 t 2 t t t r 100 t r t r t t V s s t t t r t r s t s t s rr t s t t 3 r r t t t r t t r r t s s t t2 s st t r t r s r t t s r t s t t t t r t t t r s t t t V out = 1 RC V g dt. y(t) t t t t r t s r t t e(t) = r y(t) t rr r

60 r s t t r t r r t s 2 t t r t t rr r s t 2 t s2st s ẏ(t) = 1 τ y(t)+ K t i ( ( r y t )) τ 2 dt, r τ s t t t st t K i s st t t t s t t r s t t r t r s t s2st r q t t ÿ(t) = 1 K i τẏ(t)+ (r y(t)), τ2 s st 2 st t s t r y(t) = r(t) t t t r s2st r t s t r rr s t t t s q s t V = R 1 αp in cos(2k L) = 0, s t t r s t rr r s 2 t t t t r t r r r t s t t2 r q 2 s 1 t t 5Hz r r t 3 s2st s rr t s s s t t t 3 t r t 3 r r ss t r 3 r r s r t t 10±0.1 t s t r t s t t t t r t 20V 120V t t tr 2 r 2 tr s s 3 t s r rt t t t δl = K pzt V, t st t K pzt r s s K pzt = 1µm/V t t r 3 r t π/3rad r t r t r t s t t tr s t ts 3 t r t t rr r s 2 x 1 sinα 1 cosα 1 ( ) x 2 = R sinα 2 cosα 2 sinθ, sinφ x 3 sinα 3 cosα 3 r R = 13.9mm s t r s θ s t r t r t rt 1 s φ s t r t r t r 3 t 1 s α 1 α 2 α 3 r t r s t t t r 3 r r t s r ts s t 3 t t st t s s t r t st t t r t

61 t s rr t s s t rr t 2 t tr s t t L t t r s t t rr r ss t r t t t t r s s s t r q s st r s t s2st t ss ss t r t t r q 2 f 0 = 32.29Hz t t ts t s2st s t r s s t r t r q 2 s t r s ts t r t r st t t r r t r r t r rr r s r r2 s r ts t t st rr r r r t r 2 ts 2 rst st s t t t t r r t r t t r r t r s t t r s t s r t t s t s t t tr sts t s s t t t s r 1 tr2 t t 2 2 st t s t t t st rr r t t t s t s r t s r s t t t 3 s s s s s t s t t rr r r s t r r r s r s r ts s t s r t r 11mW t t t s s t r s { V1max = 7.9V, V 1 V 1min = 0.7V; { V2max = 8.5V, V 2 V 2min = 0.7V; { Vmax = 7.5V, V V min = 6.8V; s r tr st C 1 = V 1max V 1min V 1max +V 1min = 0.84 C 2 = V 2max V 2min V 2max +V 2min = r r t s t r r C = r r t t s r ts t r s t t t r t t r r t q t s t r s t V 1 = V 1min + V 1max V 1min 2 = V 1min + V 1max V 1min 2 V 2 = V 2min + V 1max V 1min 2 = V 2min + V 2max V 2min 2 cos 2 (k L) (1+cos(2k L)) sin 2 (k L) (1 cos(2k L)).

62 t t t V s r V = V 1 V 2 = V max V min 2 rr s t cos(2k L) = 1 + V max V min 2 V max = V 1max V 2min, V min = V 1min V 2max cos(2k L), rr s t cos(2k L) = 1 2 r q t 2 t r t t r s d V d L = 2k V max V min sin(2k L) 2 K cal = 1 k( V max V min ) = m V. 2 t 2 t s r ts t t r t s t r s r t t s ts t rr r t s t t t s s s r s 2 t s t s s s t t t t s t t r t t t t r r s t t s t s r t s t t rr t t t t s σ I = 2qI, r q s t t r2 r s r t t s t s σ Itot = σi 2 +σ2 I = 2 qi. rr t t t 1 ts r t t t r r t r s t r s I = V R r V = V max V min 2 s t t t t t r R s t r s st t rst st t r s t s t s s σ δl = σ Itot di d L = σ Itot di d V d V d L t s r t r k L = π 4 t s 4qI = 1 R 2k Vmax V min 2 sin(2k L) sin(2k L) = 1 r q t t s t s s σ δl = λ qr π 2( V max V min ) = m Hz.

63 s s r ts t t s r ts t s t t tr s2st t s s r ts 1 t r 1 t 2 t r t s r q 2 F s = 100kHz r s N = t t r t s r ts s r t s 2 t r t t r K cal 2 q t r r rt t r r r t t s r ts t r s s t t r s s s t r q r s s t t2 t r q 2 r t r st s tr 23 r rst t s r t t t s tr 23 r s r t s r ts t s t s r s s r s t t t r s s r ts t t t s VX100 r s t t t s t s t t ts t s2st t t t s tr 23 r t s s s r t t t s tr 23 r s t s r q 2 F s = 81920Hz r s N = t s r t t t s s s t s r q 2 F s = 500kHz r s N = t t r s tr s t2 t t t r t t t P1 1 s t s t s r s tr s t2 t t r 1 t t t t t r s s ts s 2 ts t t r t s t s t 2 t t r t 0 st t s t t t r r r t t t t s ts s s r t r t t s st t s r r tt t r t t s s 2 s s t 1 t VX100 r r t tt r r s t P r s s t r t t t t s s s t s r 2 t r t s r s tr s s r s t t t t t r t s s2 t rst t t t s s t s t r V s s r ts r t t r t t 3 s r s t t r r t t t t r t r t r s r rt t t t t s s t r t st t r t t ss t r s t s s r t t t s V t t t s s t 2 s r t t r r t s V V 2 t t P s r t s V V 1 t t P s r t t t t 2 r r t 2 r s t s s r ts t r t t 3 s s r t r s r rt t t t t s r s 2 s r t s r ts t s s t t2 t s2st r t t t t r r s s r s t t r s s t r q s > 5kHz

64 r r s tr s t2 s r t s s t t s tr 23 r r r s t t s s t t s t r t t t t s r t r s s s t r q r s s t t2 t r q 2 t r st

65 r s s t t s r ss s r t s s t t s t s t t t s r t t t r r r t t t s s t s t s s r t s r ts t tr s r t s t t t s s r s t t t r r t t t t t tr s t t t P tr s s 2 t t t r t s 2 t t r t s st t s t P t r t r q 2 r 72.34kHz t 7.234MHz s r r t t r r t r t s s r ts r t s r q 2 F s = 100kHz s r t tr s r t V/V 1 t r P s s r rs r tt t s V/V 2 t r ts s r r t r t t t tr s r t V/V 1 s s s s s t r s s t s s t t2 t s t s s s r P 3 r r s 3 s2st s r r s t tr 3 2 t s s r s t s rt t t s t s s t s r t r t t 3 s t r t s t s t s t t t s s r r t r t s r ts t s s s s t t t r ts t tr s2st t t t t t r r t 3 s s r t r r s s t 2 rs s t s s t t2 rt r 2 t r q s t t s t t t r r r tr s r t G(s) s2st s s G(s) = Y(s) X(s), r X(s) X(s) r t tr s r t t t t s r s t 2

66 r r s t s s t t2 t s t r t r t t t r t s st t r r r s tr s r t s V/V 1 V/V 2 r t t t r t s st t r

67 r r s t tr s r t s V/V 1 V/V 2 t r t t t r t s st t r r s r ts t s s t t t t r r t 3 s2st

68 r s t t r t r t r t r s s s r t s t t r t r 2 r ts t t s tt t t rt r s st r t r t 50Ω r s ts s s r r t t t s s t 2 t r t t r K pzt r tt t t r r r t t s t r s s t t rr r t t 3 t s st s r t t r s2st t r t t r t r t r s ss t r t t r q 2 f 0 = 32.29Hz t 2 t t t s r t tr s r t t t r T (f) = 1+ 1 ( f f0 ) 2. t r t r s t r t st s r s t t t s2st t t s s t s rt t s t s t r t t t t r ss t r ss t r s st t t tr s2st s s t r t s ts s s r r t s s s 1 t s t 3 r r t t t t t r r tt t r t t t s s t r K pzt 2 10 r r t s r t t t r r tr s s s r t s t t s r t t s t s t r r s ts t s t t tr ts t r r s s t s s r ts r t t 1 t s t s t s r s s t t2 t s2st s t s

69 r r s t t t t s t t t t t r r s r ts t s s s t2 t s t t tr s r s s s t t s t s

70 s ts s r t s rst r t r 3 t t s t s t st rr r s r r s s st t r 2 t t ts s s t t2 s t s r t s ts t t rr r t r s r t r t r 3 t s st t t ts t r s r r t r t s s t t2 2 t t t r q 2 r t r st 2 10kHz t s s t t2 t t r r tr s s r s 2s tt r t t r q r t s r rt r s s t t2 t s tt r t 2kHz t s tt r t 10kHz s s t r s ts s t t t r t st t s s t 1t t r t t t tr s2st s r t s r t t r rr r s tt r t r t s s 1 t tt r t s s t t2 r s t t s s s t t2 r tt r t t r q r ts t 1 t s t s t r2 r s ts s t t t r tr s2st t 1t t r t t t s s r s t t rr r r ts s r ts t q t2 t r

71 t r s r ts t t r s r ts t t r t r rr r r r r t t r r t r2 r t rr r s t r r r t r t r t s s t s s t r t s t r rst t t t tr s2st s tt r t r t s r t r t r 3 t t t t s r t t q s t r s ts t s t t r r t r s t s str t r r t r rr r r r rr r s s s t r t r tt t r s rs SiO 2 t t r 0.3mm s t s r t r t ss s s s t r r r s st t t r 0.66mm t 0.7m s t s r t rt tr s t r t r s t t rr r tr s2st s r t t s r t r t r 3 t s t t t r r t r t r t t r s z t t rr r tr t rr r s s s t r ts r s t t r s r rr t s r t r t s s r z t tr s t ts z s t rr r t 1 s t r s r q 2 0.6Hz θ y t r ts r t rt 1 s t r s r q 2 6Hz θ x t r ts r t r 3 t 1 s t r s r q 2 9Hz

72 r t r t str t r r s t tr s2st

73 r r t s2st t 2 r r t r t s ts s2st s s rs t t rs r tr t rr r ts tr s s s 2 t r s P t r t ts t rr r t t t rs r t rr t s s r s t s t t ts tt t rr r t t rr r t rr t ts s t s t s t s ts r s r r s r s r r2 s s t t2 s s rs s t t t t t r t r s t rr r r t t r t r t t s t2 t t t s t st t t r t s t rt t s t s s s r r s t t t s s s r 2 t r r 0.1mm r s r t 0.3mm 0.6mm r s r t t r s t s st r r t s s t t2 s rst t r t r r t r t r s t r t t r t r str t t r z ts t rr r s rr t t t t rs t t s s t r s s s t t t s t r t t r s 2 t t r2 t rs s rst s t r t t ν 1p = 90Hz 3 r t ν 1z = 0.15Hz t s s

74 r t r t s t rr r r t r r t s t r s r t t t t t r s r s t t t st

75 r t t tr s2st 3 r 2 2πν 2p ±2πν 2p 1 4Q 2 p p = 2Q p z = 2πν 2z ±2πν 2z 1 4Q 2 z 2Q z r Q s t q t2 t r r r r s s { ν2p = 25Hz, Q p = 0.7, ν 2z = 300Hz, Q z = 0.5. t t tr s r t s2st t s t rs s t r t t tr s r t t r t tr s r t t tr s H = K (s 2πν 1z) ( s 2 +2πν 2z /Q z s+ ( 2π 2) ν2z 2 ) ( ), (s 2πν 1p ) s 2 +2πν 2p /Q p s+(2π) 2 ν2p 2 r K 2.7 s t t t2 r q 2 s 0.2Hz t t s2st s 2 t s t rs s s r s t r t t r 2 r t s t s t r q s t Hz s 2 s t rr t s s t t s r 1 t r t ss t 2 r t t r t ts tt t rr r rr ts ts s t s rr ts z t 2 r ±10µm θ y t 2 r ±5mrad θ x t 2 r ±50µrad

76 r t t t r t t 3 s r t rr t t P s t s st t s t s s s t 1 t t r s t rr r s t s ss t r tr s2st t t s s t t t s r t s t t s r s r t r t r 3 t ts t r s r s r t r r t t t V s s t t t t t rs t rst s s 3 r t s s 3 r t tr s r t t tr s2st s s r t t t t tr q t t t t s { ν1p = 0.001Hz ν 1z = 100Hz { ν2p = 15Hz, Q p = 5, ν 2z = 14.86Hz, Q z = 0.5, K = 0.5 t t2 r q 2 s 65Hz t t s s2st s s r rst t r ts s t r t r t t r q 2 ν = 100Hz r t s t ss t r t r t s r q 2 t t t t t rs s ts t s s s t s r t r q 2 ν = 15Hz s t r s t r q 2 t rt t t r t ss r s s t t r s s t r t ts t r s t t t r s t t s s t t t t 3 r r s r t r r t t ss t r t t r q 2 f 0 = 98Hz t s 2 s t 2 s t t 3 t rr t s s r t r t r 3 t t t r r t r

77 t t s V t t r ss s t r ss t r t r q 2 t f 0 = 3.79kHz r t r t s tr 23 r r r t r s ts 2 r t s t r ts r s t s s t t2 t s2st t s rs t r q s r t s r ts s 2 r t s t t t s r q s r t t t 2 r t s r r t t ss t2 t s t s tr 23 r t tt r r s t t t t r s r ts t r q 2 r r t s s r ts st t s s r s tr 23 r t t s r ss r t t s r s r s r r t s r ts t t s2st s t r s t r t r s t rst s r t r2 P r 3 rs s t r mbar t s s t r r P r P r r t t tr r 2 s s t r r t r2 s t t t t r r r r t r tt r t t s s2st s r t r r ss r t r r 10 4 mbar s st t2 rst r t s t s r t t s s t t2 t s2st r r t s r t t t s t s s t r q r ts s s t t m/ Hz t r q 2 r 2 10kHz t r t ss 2 t rst r t t t t r r t r 1 3 t tr st 2 2 t t 3 t t s t t t t t t r { V1max = 3.8V, V 1 V 1min = 1.4V; { V2max = 3.5V, V 2 V 2min = 1.4V; V { Vmax = 2.4V, V min = 2.1V; s r tr st C 1 = 0.46 C 2 = 0.43 t r t t r s K cal = m/v 2 r s s s t r t t t 1 t s r

78 r s r ts t s s t t2 t s2st t t t t P t r r t s tr 23 r r s s t s r ts t s s s t t2 t t t t ss t r r t s tr 23 r s s t r s r q 2 tr t t t t s s s ss r s s t s s r ts r t t t ss t r s ss r2 t r t r q r s s t t2 t t t t ss t r t s r t s t 2 t s tr 23 r r s r s r q s r s r s2st s s t r t r t ts t s2st s t t t s r q 2 r r r s r q 2 r2 s2st s r t r s r q s r t r s t ss r t s t s2st r t s t s r s t s2st s 1 t t r s r q s t t t r t r s s s s t 1 t t r s r s t rr r r 2 t t t (n,m) r n st t s r t r t rs m st t s r t r r r s s t r s r t r t s t rr r t r q 2 r t r st < 10kHz t r r s r tt r 2 tt r 2 t r r t s rs tt t rr r t s t s2 tr s t t tt r 2 s t r t r t t s t s r t t s r s r r s s s t t r t s t r t t

79 r s t r r t r s t tt r 2 r t r rr r r rr r s t rr r t t2 t st r t t r r t r t s r s t t Ta 2 O 5 t s ss 20kg t r 35cm s r ts ts t2 t rs r r r t t r t r r t r t r s ts r st t r s t s r t r t r t r r t r t r s r q s t rr r tt r t s t t s s r t 1t r r r s r q s t t t r s ts s t r s r r r t t r s r q s t rr r r s t 1 t t t t r s

80 r s t tt r 2 r t r s t tt r 2 5 r t r s t tt r 2 r t

81 r q 2 3 tt r 2 (13.5±0.1) 10 6 tt r 2 (3.6±0.2) 10 6 r (1.5±0.9) 10 6 tt r 2 5 (4.6±0.1) 10 4 tt r 2 s t r s r q s t t2 t r t rr r sr t r r q s t s r r t r q s s r t r s s r s r r t s t t t rr r t r t r s t r t t 1 t r s r q 2 r s t t t s s t s s s s t t rr r t r q s rr s t t s s t t r t r q 2 rst t t t r q 2 s r t t t t s s t s 2 r s t t 1 t t s s s t t t r q 2 t r s r q s r t r r s r t 2 t t r s s r ts t 2 t r r t t r t q t2 t r s t r t s ss s t s t s r t 2 t s t t r t s s s t t r s r q 2 ν 0 t t rr r t r s t t s t st t 1 t t s st rt t s r s r t t s s t s t 2 A(t) = A 0 e t τ cos(ωt). s r ts s t r s r q s t 3kHz 8kHz t s t 2q st s t r t s r t t s r q s t 6kHz 16kHz rr s t s t s t 133ms 5ms t s s t s r t s rt t t t t 2 r t s r 2 t t t s t t s tr 23 r r s s t r 2 s tr 23 r t s t s t rs t 23 r t ss s t r ss t r t t s rt t s s t s s s s t r q 2ω d st q t t r s r q 2 r s t t 1 r 2q st t r st t s t t t r2 s 1 t 2 r str t t s r q 2 s t st t t 1 r q 2 t s r s t s tr 23 r s N 800 s t = N ν, r t s t s t ν s t s r q 2

82 r r 2 s tr 23 r t t t A(t) = A 0 e t τ cos(ωt)cos(ωd t) = 1 2 A 0e t τ (cos(ω ωd )t+cos(ω +ω d )t). t s rt t t t t t t 1 s t r t t s s t 3 t s t s s s s t t s s t t t s s s r2 st r t s t 1 q 2 st r t t r r t t t rs t rst s ss t s s t t r t ss t rs t r q s r ω i = ω 0 ω d t t t r r s t r s s s ω ω d A(t) 1 2 A 0e t τ. 2 s r t s t 1s t t t s t s r r 2 st t r t s r t t t 2 t t t t r s s t r str t s s 1 t 2 r t st t t 2 t τ 2 r r t t t t 1 s 1 s t s s r ts r r s r s t t 2 s t r r t t t t q t Q = πν 0 τ, t t s r q t t s s s t s r s s r t r ss r mbar t t r s ts ν 0 = Hz tt r 2 τ = s Q = ν 0 = Hz tt r 2 τ = 540.6s Q =