Question

A particle undergoing simple harmonic motion has time dependent displacement given by x(t) = A sin`(pit)/90`. The ratio of kinetic to the potential energy of this particle at t = 210s will be ______.

Options

• `1/9`

• 1

• 2

• `1/3`

Answer 1

A particle undergoing simple harmonic motion has time-dependent displacement given by x(t) = A sin`(pit)/90`. The ratio of kinetic to the potential energy of this particle at t = 210s will be `underlinebb(1/3).`

Explanation:

Kinetic energy, k = `1/2momega^2A^2cos^2omegat`

Potential energy, U = `1/2momega^2A^2sin^2omegat`

`k/U = cot^2omegat = cot^2  pi/90(210) = 1/3`