This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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Answer
\frac{\dot{x}}{r_p}$.
Step 1: Define the generalized coordinate and express velocities of all components. Let the generalized coordinate be the displacement of mass . The generalized velocity is .
• Mass : Its velocity is . • Pulley (): The string connecting mass to the pulley implies that the tangential velocity of the pulley's edge is . The angular velocity of the pulley is . • Rigid link 1 (): This link rotates with the pulley about O. Its length is . Its angular velocity is $\dot
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Define the generalized coordinate and express velocities of all components. Let the generalized coordinate be the displacement x(t) of mass m.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.