A block of mass (m) is attached to a spring of stiffness (k) and viscous damper of

Question:

A block of mass \(m\) is attached to a spring of stiffness \(k\) and viscous damper of damping coefficient \(c\) and slides on a horizontal surface with a coefficient of friction \(\mu\). Let \(x(t)\) represent the displacement of the block from equilibrium.

(a) Derive the differential equation governing \(x(t)\).

(b) Solve the equation and sketch the response over two periods of motion.

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