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Question

A rod of length l and mass m, pivoted at one end, is held by a spring at its mid-point and a spring at far end. The springs have spring constant k. Find the frequency of small oscillations about the equilibrium position.
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Solution
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Restoring torgue τ=(klθ)l(kl2θ)l2=54kl2θ
Now, (ml23)α=(54kl2)θ
f=12παθ=12π15k4m

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