Question

Assume at $x=x_2,u\left(x\right)$ is constant. Slope $\frac{-du}{dx}=0$. The particle is displaced slightly from $x=x_2$. Then:

• A. particle will return back to $x_2$ after oscillating.
• B. particle will move further away from $x_2$.
• C. particle will stay at $x_2$.
• D. particle will come to a point where $\frac{-du}{dx}$ is maximum or minimum.

Answer 1

The correct option is B particle will move further away from $x_2$.

Since Force is 0, the particle is in equilibrium at ${x=x}_2$. But in the surrounding of $x_2$ also, $F=0$, and hence the particle is in neutral equilibrium. It will not move when displaced slightly.