Question

A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be ______.

Options

• 1 : 1

• 2 : 1

• 1 : 4

• 1 : 3

Answer 1

A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be 1 : 3.

Explanation:

In SHM, for a displacement x and amplitude A:

Potential energy (P.E.) = `1/2 kx^2`

Kinetic energy (K.E.) = `1/2 k (A^2 - x^2)`

The question states that the displacement is half the amplitude:

x = `A/2`

P.E. = `1/2 k (A/2)^2`

= `1/2 k A^2/4`

K.E. = `1/2 k (A^2 - (A/2)^2)`

= `1/2 k (A^2 - A^2/4)`

= `1/2 k (3A^2)/4`

`(P.E.)/(K.E.) = (1/2 k A^2/4)/(1/2 k (3A^2)/4)`

= `1/3`

= 1 : 3