Question

A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k. The plank is displaced by a small angle 8 from its horizontal equilibrium position and released. The angular frequency of the subsequent simple harmonic motion is :

• A.
• B. $\sqrt { \frac { \mathrm { k } } { 3 \mathrm {~m} } }$
• C.
• D. $\sqrt { \frac { \mathrm { k } } { \mathrm { m } } }$

Answer 1

Answer: (A)

Answer 2

Using torque equation about the pivot, when the rod is displaced by small angle $\theta$ from its horizontal equilibrium

position -k(Lθ) = $\frac { \mathrm { mL } ^ { 2 } } { 3 } \alpha$

α = -

ω =

Torque of gravitational force is not taken into account as it has been balanced by torque of spring force due to initial

compres­sion in equilubrium position.