A body of mass m is moving in one dimension under the influence of a conservative force with a potential energy given by U(x). Show that the body, when displaced slightly from a point of stable equilibrium at x = x0, will experience a restoring force proportional to its displacement, the force constant being

Suppose the potential energy has the form

where c and a are positive constants. Sketch this potential and the force resulting from it Find the position of stable equilibrium and calculate the angular frequency of small oscillations about this position.

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