A simple pendulum of Length L and Mass M has a spring of force constant k connec

Question

A simple pendulum of Length L and Mass M has a spring of force constant k connected to it at a distance of h below its poin of suspension. Find the frequency of vibration of the system for small values of the amplitude (Assume the vertical suspension of Length L is rigid, but neglect its mass.)

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A simple pendulum of Length L and Mass M has a spring of force constant k connected to it at a distance of h below its poin of suspension. Find the frequency of vibration of the system for small values of the amplitude (Assume the vertical suspension of Length L is rigid, but neglect its mass.)

Explanation / Answer

compression=theta*h

so,

balanciing torque,

mglsinx-k*(theta*h)*h=ml^2*alpha

or (mgl-kh^2)=mw^2

or w=((mgl-kh^2)/m)^0.5

so f=w/2pi

=(1/2pi)*((mgl-kh^2)/m)^0.5

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