Question

a body is executing shm of amplitude 1n at what distance from mean position its kinetic energy and potential energy are equal?

Answer 1

The expression for kinetic energy is,

K = mω²(a² - y²) / 2

and that for potential energy is,

U = mω²y² / 2

where,

• m = mass of the particle

• ω = angular frequency

• a = amplitude

• y = displacement

In the question, in the simple harmonic motion of the particle, there exists a point which is y distance away from the mean position such that the kinetic energy and potential energy of the particle are numerically equal. Thus,

K = U

mω²(a² - y²) / 2 = mω²y² / 2

a² - y² = y²

a² = 2y²

y = ± a / √2

Displacements can be of opposite directions, that's why there are both signs for y.