Question

The Advanced Laser Interferometer Gravitational-wave Observatory (Advanced LIGO) experiment was recently credited with confirming the existence of graviational waves for the first time. Key to its success was the development of a vibration isolation system to eliminate motion of lasers and mirrors. One requirement of the isolation system was to reduce seismic disturbances (base excitation) that oscillate at 0.16 Hz to produce system oscillations with a displacement transmissiblility is 1/10. The mass of the isolation mount is to be 100 kg: assume a damping ratio of 0.1 1. x(t) 0.1 meq meq 100 kg excitation frequency Steady-state motion (Ignore gravity) 0.16 Hz keq y(t) - yo sin(o t) Find: a) (3 pts) Using the expression for displacement transmissibility (eq 2.5.16), find the value of frequency ratio, r, that will produce a displacement transmissibility of 1/10. b) (1 pt) Compute the corresponding undamped natural frequency, Wn c) (1 pt) Find the corresponding values of equivalent stiffness, keq, and equivalent damping, Ceq.

Answer 1

ky o.16 100 Vn Claupsing nati vsk

2 IKm 0 2 x1 3) &f Hente th ry