Paragraph : A particle vibrates in S.H.M. along a straight line. Its velocity is 4 cm/s when its displacement is 3 cm and velocity is 3 cm/s when displacement is 4 cm.
Starting from origin a body oscillates simple harmonically with a period of 2 s. After what time will its kineti energy be 75% of the total energy.

Options

A. `(1)/(6)s`
B. `(1)/(4)s`
C. `(1)/(3)s`
D. `(1)/(12)s`

Answer

A

Explanation

`K.E.=(75)/(100)T.E.`
`implies(1)/(2)m omega^(2)(r^(2)-y^(2))=(3)/(4)((1)/(2)m omega^(2)r^(2))`
`r^(2)-y^(2)=(3)/(4)r^(2)" "impliesy=r//2`
Now `y=r sin omegatimplies( r )/(2)=r sin" wt"impliessin omegat=(1)/(2)`
`implies" "omegat=pi//6" "implies(2pi)/(T)t=(pi)/(6)" "implies" "t=(T)/(12)`
So correct choice is (a).