Starting from the mean position a body oscillates simple harmonically with a period of 2 s.

Options

A. Its kinetic energy will become 75% of the total energy after `1/6` s
B. Its kinetic energy will become 75% of the total energy after `1/12` s
C. Magnitude of its momentum will become half of initial after `1/3` s
D. Magnitude of its momentum will become half of initial after `1/6` s

Answer

A, C

Explanation

`v=Aomegacos(omegat)`
forKE=75% of `KE_(max)`
`v=sqrt(3)/2 of v_(max)`
`sqrt(3)/2Aomega=Aomegacos((2pi)/2xxt)Rightarrow t=1/6sec`
or `P=P_(max)//2`
`Rightarrow 1/2=cos((2pi)/2xxt)Rightarrowt=1/3`