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# Problem/CM-01008 Periodic Motion

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Question : Find potential if the force acting on a particle in one dimension is  $$F(x) = m \omega_0^2(x-2bx^3).$$ Determine the potential energy asuming $V_0=0$ and show that the period of oscillations as a function of amplitude $a$ is $$T =\frac{2}{\omega_0}\int_{-a}^a \frac{dx}{(a^2-x^2)(1- b(a^2+x^2))}$$
and that for small $a$  $$T = \frac{2\pi}{\omega_0}(1+ \frac{3}{4}b a^2)$$

cm-que-01008

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