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In Fig. AB is a horizontal plank of len...

In Fig. AB is a horizontal plank of length 1 and mass m. It is pivoted at one end and the other end is attached to a spring of force constant k. The moment of inertia of the plank about the pivot is `1/3ml^2` ml. If the plank is displaced by a small angle `theta` from the horizontal and released show that its motion is shm. What is the period of oscillation ?

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The correct Answer is:
`T=2pisqrt((m)/(3k))`
`I"d"theta^2//dt^2=-kxxxlcostheta=kl^2theta//dt^2=-kt^2thetaxxkt^2thetaxx3lml^2=-(3k//m)theta T = 2pi sqrt(m//3k)`
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