A rod of mass M and length L is hinged at one end and carries a particle of mass m at its lower end. Springs k₁ and k₂ are attached at distances a and b from the hinge as shown. Find the frequency of small oscillations.

Question

G1 Physics · Accepted Answer

For a small angular displacement θ, spring extensions are aθ and bθ. Restoring torque is (k₁a²+k₂b²)θ. Moment of inertia about the hinge is I=(1/3)ML²+mL²=L²(m+M/3). Hence f=(1/2π)√[(k₁a²+k₂b²)/(L²(m+M/3))]. Correct option: 1.