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.
The displacement of an object attached to a spring and executing simple harmonic motion is given by `x=2xx10^(-2)cos pi t` metres. The time at which the maximum speed first occurs is :

Options

A. 0.75 s
B. 0.125 s
C. 0.25 s
D. 0.5 s

Answer

D

Explanation

`x=2xx10^(-2)cos pi t`.
Comparing it with standard from `x=r cos omegat`. We have
`omega=piimplies(2pi)/(T)=pi`
`implies" "T=2` second
Now in time `t=(T)/(4)` the particle goes from extreme position to mean position where K.E. becomes maximum. `:." "t=(2)/(4)=0.5`
So, correct choice is (d).