Problem B$-8-9$

Consider the mechanical system shown in Figure $8-29.$ It is at rest for The pendulum $m_2$ is supported by mass $m_1.$ which vibrates because of an elastic connection. Derive the equations of motion for the system. The displacement $x$ is measured from the equilibrium position for The angular displacement $$ is measured from the vertical axis passing through the pivot of the pendulum.Figure $8-29$ Mechanical system.

Assuming the initial conditions to be $x(0)=0\mathrm{.}1m,x^{}(0)=0\frac{m}{s},(0)=0$rad. and ${}^{}(0)=0ra\frac{d}{s},$ obtain the motion of the pendulum. Assume also that $m_{t_1}=10kg,m_2=1kg,k=250\frac{N}{m},$ and $l=1m.$