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Question

A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring constants k. The springs are fixed to rigid supports as shown in the figure, and rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle θ in one direction and released. The frequency of oscillation is?
1010207_8f5439ee66a9403bbbe3e545ca4069fe.png

A
12π2kM
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B
12πkM
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C
12π6kM
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D
12π24kM
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Solution

The correct option is C. 12π6kM.

Restoring torque =2×K(l2θ)l2=Id2θdt2

Now, d2θdt2=kl22(θ)Ml212

From the relation, α=ω2θ we have

ω=6kM
Frequency, f=ω2π=12π6kM

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