Question

A body oscillates simply harmonically with a period of 2 seconds, starting from the origin. Its kinetic energy will be 75% of the total energy after time ______

`(sin30^circ = cos60^circ = 1/2)`

Options

• `1/6s`

• `1/3s`

• `1/12s`

• `1/4s`

Answer 1

A body oscillates simply harmonically with a period of 2 seconds, starting from the origin. Its kinetic energy will be 75% of the total energy after time `underline(1/6s)`.

`(sin30^circ = cos60^circ = 1/2)`

Explanation:

T = 2 sec

`3/4`TE = PE

`3/4(1/2 momega^2A^2) = 1/2momega^2(A^2 - x^2)`

`3/4A^2 = A^2 - x^2`

∴ `x^2 = A^2 - 3/4A^2 = A^2/4`

∴ `x = A/2`

∴ x = A sin ωt

`A/2 = A/2 sin  (2pi)/2 . t = sin  pi/6`

∴ `pit = pi/6`

∴ `t = 1/6sec`