A body is executing S.H.M. when its displacement from the mean position is 4 cm and 5 cm, the corresponding velocity of the body is 10 cm/sec and 8 cm/sec. Then the time period of the body is

Options

A. `pi sec`
B. `(pi)/(2)sec`
C. `2pi s`
D. `(3 pi)/(2) sec`

Answer

A

Explanation

`v=omegasqrt(A^(2)-x^(2)) therefore v^(2)=omega^(2)(A^(2)-x^(2))`
`omega " For " x= 4cm, 100 = omega^(2)(A^(2)-16)=omega^(2)A^(2)-16 omega^(2)`
`therefore 100-64= - 16omega^(2)+25 omega^(2)=9omega^(2)`
`therefore 36=9 omega^(2) therefore omega =2`
and `T=(2pi)/(omega)=(2pi)/(2) therefore T= pi s`