A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (see figure). Derive the equation of motion for the pendulum. Find the frequency and period of vibration of the system for small values of the amplitude. Assume the vertical suspension of length L is rigid, but ignore its mass.

A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension (see figure). Derive the equation of motion for the pendulum. Find the frequency and period of vibration of the system for small values of the amplitude. Assume the vertical suspension of length L is rigid, but ignore its mass.

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