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Starting from the origin a body osillate...

Starting from the origin a body osillates simple harmonicall with a period of 2 s. A fter what time will its kinetic energy be 75% of the total energy?

A

`(1)/(4) s`

B

`(1)/(3)s`

C

`(1)/(12)s`

D

`(1)/(6)s`

Text Solution

Verified by Experts

The correct Answer is:
D
Since , Ke = (0.75 ) E
`rArr (1)/(2) m omega ^(2) A^(2) cos^(2) ( omega t) = (3)/(2) ((1)/(2) m omega ^(2) A^(2))`
`rArr cos ^(2) ((2 pi t)/( T) t) = (3)/(4)`
`rArr cos ((2 pi)/( T ) t) = ( sqrt(3))/( 2)`
`rarr (2 pi )/( T) t = (pi)/( 6) rArr t = (T)/( 12)`
When T = 2 s `rArr t = (1)/(6) s `
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