A body is executing SHM. When the displacement from the mean position is `4 cm` and `5 cm`, the corresponding velocities of the body is `10 cm//s` and `8 cm//s`. Then , the time period of the body is

Options

A. `2pi sec`
B. `pi//2sec`
C. `pi sec`
D. `3pi//2 sec`

Answer

C

Explanation

`v=omegasqrt(A^(2)-x^(2)) Rightarrow 10=omegasqrt(A^(2)-4^(2))`
`Rightarrow 8=omegasqrt(A^(2)-5^(2)) Rightarrow ((10)/(8))^(2)=(A^(2)-4^(2))/(A^(2)-5^(2)) Rightarrow (25)/(16)=(A^(2)-16)/(A^(2)-25)`
`25A^(2)-625=16a^(2)-256 Rightarrow 9A^(2)=625-256=369 Rightarrow A^(2)=(369)/(9)` `omega=(8)/(sqrt((369)/(9))-25)=(8xx3)/(sqrt369-225)=(8xx3)(12)=2 Rightarrow T=(2pi)/(omega)=pis`.