In SHM, amplitude of kintetic energy is `((l)/(4))^(th)` of the total energy at a displacement equal to:

Options

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

Answer

B

Explanation

In SHM,
Kinetic energy, `k=(1)/(2) m omega A^(2)(A^(2)-x^(2))`
Total energy `E=(1)/(2)m omega^(2)A^(2)`
As, `k=(E)/(4)`
`:. (1)/(2)m omega^(2)(A^(2)-x^(2))=(1)/(4)((1)/(2)m omega^(2)A^(2))`
(or) `4A^(2)-4x^(2)=A^(2)`
(or) `4x^(2)=3A^(2)x`
(or) `x=(sqrt(3))/(2)A`