(a) A particle of mass m moves under the influence of the potential energy V(x) = (1 – a x)e-ax in the region x > 0 and a > 0. Determine (a) the location of the equilibrium points, (b) the nature of the equilibrium, and (c) the natural frequency of

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(a) A particle of mass m moves under the influence of the potential energy V(x) =
(1- a x)e-ax in the region x > 0 and a > 0. Determine (a) the location of the
equilibrium points, (b) the nature of the equilibrium, and (c) the natural frequency of
the oscillations for motion restricted to small displacement in the neighborhood of the
equilibrium.
Transcribed Image Text:(a) A particle of mass m moves under the influence of the potential energy V(x) = (1- a x)e-ax in the region x > 0 and a > 0. Determine (a) the location of the equilibrium points, (b) the nature of the equilibrium, and (c) the natural frequency of the oscillations for motion restricted to small displacement in the neighborhood of the equilibrium.
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