Question

When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is ______.

Options

• 1 : 3

• 2 : 1

• 3 : 1

• 1 : 2

Answer 1

When the displacement of a particle executing simple harmonic motion is half its amplitude, the ratio of its kinetic energy to potential energy is 3 : 1.

Explanation:

x = A cos ωt

x = `"A"/2`

we get ωt = 60°

`"KE"/"PE" = (1/2 "m"ω^2"A"^2 sin^2 ω"t")/(1/2 "m"ω^2"A"^2 cos ω"t")`

= tan² ωt

= tan² 60°

= 3