A particle is executing simple harmonic motion with amplitude A. When the ratio of its kinetic energy to the potential energy is `(1)/(4)`, its displacement from its mean position is

Options

A. `(2)/( sqrt5) A`
B. `(sqrt3)/(2) A`
C. `(3)/(4) A`
D. `(1)/(4) A`

Answer

A

Explanation

Given, `(KE)/(PE) = (1)/(4)`
But we know that in SHM
`KE = (1)/(2) K (A^2 - x^2)`
and `PE = (1)/(2) Kx^2`
Hence, `((1)/(2) K (A^(2) - x^(2) ) )/( (1)/(2) Kx^2) = (1)/(4)`
`4A^(2) - 4x^(2) = x^(2)`
`4A^(2) - 5x^(2) = 0`
`4A^(2) = 5x^(2)`
`x^(2) = (4)/(5) A^2`
`x= (2)/( sqrt5) A`