Find the equivalent mass of the system shown in Fig. 1.38, where the rigid link 1 is attached to the pulley and rotates with it.

Step 1: Define the generalized coordinate and express velocities of all components.
Let the generalized coordinate be the displacement $x(t)$ of mass $m$. The generalized velocity is $\dot{x}(t)$.

• Mass $m$: Its velocity is $\dot{x}$.
• Pulley ($J_p$): The string connecting mass $m$ to the pulley implies that the tangential velocity of the pulley's edge is $\dot{x}$. The angular velocity of the pulley is $\dot{\theta}_p = \frac{\dot{x}}{r_p}$.
• Rigid link 1 ($m_1$): This link rotates with the pulley about O. Its length is $l_1$. Its angular velocity is $\dot