The kinetic energy of paritcle executing SHm will be equal to `((1)/(8))^(th)` of its potential energy when its displacement from the mean position is (Where A is the amplitude) :

Options

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

Answer

A

Explanation

Kinetic energy when the displacement of the particle is x is given by,
`k=(1)/(2) m omega^(2)(A^(2)-x^(2))`
Potential energy at this instant is given by,
`U=(1)/(2)m omega^(2)x^(2)`
As,`k=(1)/(8)U`
`:.(1)/(2)m omega^(2)(A^(2)-x^(2))=(1)/(8)((1)/(2)m omega^(2)x^(2))`
(or) `(A^(2)-x^(2))=(x^(2))/(8)`
On rearranging, we get,
`x=(2sqrt(2))/(3)A`