Question

The ratio of the maximum kinetic energy to the maximum potential energy of a bob of a simple pendulum executing small oscillations is

• A. 1 : 1
• B. 1 : 2
• C. 2 : 1
• D. 1 : 4
• E. 4 : 1

Hint:

In simple harmonic motion, the maximum kinetic and potential energies are equal at different points in the motion.

Answer 1

The Correct Option is A

In simple harmonic motion, the kinetic energy and potential energy of the pendulum are equal at the point of maximum amplitude (extreme displacement). \[ {Kinetic Energy} = \frac{1}{2} m v^2 \quad {and} \quad {Potential Energy} = \frac{1}{2} k x^2 \] At the extreme position, all the energy is potential, and at the equilibrium point, all the energy is kinetic. 
Therefore, the ratio of the maximum kinetic energy to the maximum potential energy is 1:1. 
Hence, the correct answer is (A).