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

Answer

C

Explanation

Kinetic energy when the displacement of the particle is x is given by `K=(1)/(2)momega^(2)(A^(2)-x^(2))`
Potential energy at this instant is given by `U=(1)/(2)momega^(2)x^(2)`
As `K=(1)/(8)U therefore (1)/(2)momega^(2)(A^(2)-x^(2))=(1)/(8)((1)/(2)momega^(2).x^(2))`
or `(A^(2)-x^(2))=(x^(2))/(8)orx=(2sqrt(2))/(3)A`