Question

In a simple harmonic motion
(a) the maximum potential energy equals the maximum kinetic energy
(b) the minimum potential energy equals the minimum kinetic energy
(c) the minimum potential energy equals the maximum kinetic energy
(d) the maximum potential energy equals the minimum kinetic energy.

Answer 1

In Simple Harmonic Motion, Relation of Kinetic and Potential energy is given by the formula,

Kinetic Energy = 1/2 k(A² - x²)

Potential energy = 1/2 kx²

For maxima, and minima in Kinetic and Potential energy.

________________________

Kinetic Energy.

Maximum when x = 0.

K.E. = 1/2k(A² -0²) = 1/2kA²

Minimum when x = A.

K.E. = 1/2k(A² - A²) = 0

_________________________

Potential Energy,

Maximum when x = ± A

P.E. = 1/2kA²

Minimum when x = 0

P.E. = 0

From this we can see that minimum potential energy equal the minimum kinetic  energy and Maximum Potential energy equal the maximum kinetic energy.

Thus, Option (a). and (b) are correct.

Hope it helps.