A particle is vibrating simple harmonically with amplitude `'a'`. The displacement of the particle when its energy is half kinetic and half potential is.

Options

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

Answer

B

Explanation

Kinetic energy `=` Potential energy
`(1)/(2) m omega^(2) (a^(2) - y^(2)) = (1)/(2) m omega^(2) y^(2)`
`a^(2) - y^(2) = y^(2)`
`2y^(2) = a^(2) rArr y = +- (a)/(sqrt(2))`