Problem $35$

The rigid bar $AB$ shown at the right is hinged at end A and is excited by the force in damper $BC,$ where the motion of $C$ is specified to be $z(t).$

a$.$ Determine the equation of motion of the bar in terms of the angular rotation of the beam $(t),$ which is taken to be positive counterclockwise. Assume small rotations.

b$.$ Determine the frequency response function $H_z().$

c$.$ Calculate the steady$-$state response $(t)$ for the motion of point $C$ specified as $z(t)=10cos(5t)+4$