A particle oscillates about the stable equilibrium position `x_(0)` with a small amplitude subjected to a force that has an associated potential energy `u(x)`. Which of the following about `u(x)` is true (no implsive force)

Options

A. `u(x)` must be symmetric about `x_(0)`
B. `u(x)` must have a minima at `x_(0)`
C. `u(x)` may have maxima at `x_(0)`
D. `u(x)` may be position in the vicinity of `x_(0)`

Answer

B, D

Explanation

The only need for oscillation is potential energy should have a minima and for the amplitude given it should not cross the valley.