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, an

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

TestHub · Accepted Answer

​ Restoring torque = − ( 2 k x ) ⋅ 2 L ​ α = − I k L ( L /2 θ ) ​ = − [ M L 2 /12 k L 2 /2 ​ ] ⋅ θ ​ ∴ f ​ = − ( M 6 k ​ ) θ = 2 π 1 ​ ​ θ α ​ ​ ​ = 2 π 1 ​ M 6 k ​ ​ ​

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