When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude a is

Options

A. `(A)/(4)`
B. `(A)/(3)`
C. `(A)/(2)`
D. `(A)/(sqrt(2))`

Answer

D

Explanation

Potential energy of particle, `U = (1)/(2)m omega^(2)y^(2)`
Potential energy of maximum particle, `E = (1)/(2)m omega^(2)A^(2)`
According to given position, the potential energy, `U = (E)/(2)`
or `(1)/(2)m omega^(2)y^(2)=(1)/(2)xx(1)/(2)m omega^(2)A^(2)`
`rArr" "y^(2)=(A^(2))/(2),y=(A)/(sqrt(2))`