1. LIGO-G050442-00-Z1 E2e modeling of violin mode S. Yoshida Southeastern Louisiana University V. Sannibale M. Barton, and H. Yamamoto Caltech LIGO NSF: PHYS-0354942 LLO

2. 2 Violin model N oscillators (massless string + bob) L w1, T w1 L w2, T w2 Optic as final oscillator ii State Space representation (ABCD matrix) V. Sannibale (LIGO I, Maple) M. Barton (AdvLIGO, Mathematica) (Wire length, tension)

3. 3 Two State Space boxes (LIGO I) New dynamics included: Coupling among 1)pos, pitch, yaw & violin 2)bounce, roll & side Sus pt motion Actuation force (COIL) Opt motion Pos* Pitch Yaw Bounce** Roll side 3DSusViolin.box (3DSus primitive) * Under testing, ** Will be added soon.

4. 4 LOS/SOS violin.box Controller.box 3DSusViolin.box Seismic noise Floor motion DAQ & table motion model* Violin Optic OSEM sensor Optical Lever Length Sensing Control/Optical Spring *Aug04/March05 LSC meeting T. Findley, et al., G050219-00-D S. Yoshida et al., T030159- 00-D Actuation (coil) force

5. 5 White Noise Input to sus point (free hanging) Split due to wire asymmetry

6. 6 Step Input to sus point z (free hanging) 3Dsus primitive3DsusViolin.box Sus point z to Opt Yaw coupling: due to wire asymmetry Z to Opt pos Z to Opt pitch Z to Opt yaw 10 -10 0 0.2 -0.2 0 2 0 1 2 0 1 10 - 10 0 0.2 -0.2 0 Time (s) Z

7. 7 Step Input to sus point yaw (free hanging) 3Dsus primitive3Dsus_Violin.box Yaw to Opt pos Yaw to Opt pitch Yaw to Opt yaw 1 0 x10 -3 1 0 6 -6 0 2 0 1 1 0 Time (s) Sus point Yaw to Opt Pos/Pitch coupling: due to wire asymmetry 2 0 1

8. 8 Step Input to sus point z (pitch local damp on) Time (s) Free hang Local-damped coil force Z to Opt pos Z to Opt pitch Z to Opt yaw 4 -4 0 3 1 0.4 -0.4 0 Frequency (Hz) yaw pitch pos

9. 9 Step Input to sus point yaw (yaw local damp on) Time (s)Frequency (Hz) coil force Free hang Local-damped Yaw to Opt pos Yaw to Opt pitch Yaw to Opt yaw x10 -4 x10 -3 3 1 0.4 -0.4 0 2 -2 0

10. 10 Plan for AdvLIGO - HAM, BSC boxes stack models needed! - Suspension (Mark Barton’s model, 6DOF x stages, + violin) numerical experiment of MC performance - Detailed analysis location of suspension on HAM table