A delicate instrument of mass m must be isolated from excessive vibration of the ground, w...

A delicate instrument of mass m must be isolated from excessive vibration of the ground, which is described by the function u(t) = A sin ω0t.To do so, we need to design a vibration isolating mount, modeled by the spring and dashpot system shown.

(a) Find the equation of motion of the instrument and reduce it to standard form.

(b) Find the steady-state response y(t).

(c) Find the displacement transmissibility, i.e., the response amplitude D divided by A, where A is the amplitude of the ground’s vibration.

Figure P9.66