The potential energy of a simple harmonic oscillator when the particle is half way to its end point is
(where, E is the total energy)

Options

A. `(1)/(4)`E
B. `(1)/(2)`E
C. `(2)/(3)`E
D. `(1)/(8)`E

Answer

A

Explanation

Potential energy of a simple harmonic oscillator,
`U = (1)/(2)m omega^(2)y^(2)`
When the particle is half way to its end point, i.e. At half of its amplitude, then, `y = (A)/(2)`
Hence, potential energy,
`U = (1)/(2)m omega^(2)((A)/(2))^(2)=(1)/(4)((1)/(2)m omega^(2)A^(2))=(E)/(4)`