The kinetic energy and potential energy of a particle executing simple harmonic motion will be equal, when displacement (amplitude `=a`) is

Options

A. `(A)/(2)`
B. `Asqrt(2)`
C. `(A)/(sqrt(2))`
D. `(Asqrt(2))/(3)`

Answer

C

Explanation

`K.E.=P.E.`
`(1)/(2)momega^(2)(A^(2)-x^(2))=(1)/(2)momega^(2)x^(2)`
`A^(2)-x^(2)=x^(2)`
`A^(2)=2x^(2)`
`A=sqrt(2)xtherefore x=(A)/(sqrt(2))`