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Net Force

If the partic...

Question

If the particle mass m moves in a potential energy $U = u_{0} - a x + b x^{^{2}} w h e r e u_{0}$ , a and b are positive constant. Calculate the force constant, frequency of the particle of equilibrium.

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Solution

$U = u_{o} - a x + b x^{2}$

$F = - \frac{d U}{d x}$

$⟹ F = - 2 b x + a$

Hence, force constant $k = 2 b$

And, frequecny $f = \frac{1}{2 π} \sqrt{\frac{k}{m}} = \frac{1}{2 π} \sqrt{\frac{2 b}{m}}$

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