# Thread: Equilibria and Oscillations question

1. ## Equilibria and Oscillations question

stuck again...

A particle of mass m = 1 moves along the x-axis under a force whose potential is:

V(x) = (1 - x^2)*e^(-(x^2)/4)

Sketch the function V against x, find equilibrium positions and stability. Determine the periods of small oscillations about the stable equilibrium point(s). If the particle is started at x = sqrt(5) with speed U, determine the ranges of U for which the particle (i) oscillates, (ii) escapes to
+infinity and (iii) escapes to −infinity.

Many thanks

2. Originally Posted by callumh167
stuck again...

A particle of mass m = 1 moves along the x-axis under a force whose potential is:

V(x) = (1 - x^2)*e^(-(x^2)/4)

Sketch the function V against x, find equilibrium positions and stability. Determine the periods of small oscillations about the stable equilibrium point(s). If the particle is started at x = sqrt(5) with speed U, determine the ranges of U for which the particle (i) oscillates, (ii) escapes to
+infinity and (iii) escapes to −infinity.

Many thanks
The force on the particle is:

$F(x)=\left. \frac{dV}{dx}\right|_x$

The possible equilibrium positions are where there is no force, and so correspond to the extrema of $V(x)$ .

Stable equilibria are minima of $V(x)$.

RonL