The potential energy of a particle oscillating along x-axis is given as
`U=20+(x-2)^(2)`
Here, `U` is in joules and `x` in meters. Total mechanical energy of the particle is `36J`.
(a) State whether the motion of the particle is simple harmonic or not.
(b) Find the mean position.
(c) Find the maximum kinetic energy of the particle.

Options

A. 24 J
B. 36 J
C. 16 J
D. 20 J

Answer

C

Explanation

E = 36 J
`U = 20 + (x - 2)^(2)`
`U_(min) = 20` when x = 2 for all other x values, `U gt 20`
`K_(max) = E - U_(min) = 36 - 20 = 16 J`