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A praticle of mass m is executing osc...

A praticle of mass m is executing oscillation about the origin the on the x-axis .Its potenial energy is `U(x)=k(x)^(3)`, where k is a positive constant . It the amplitude of ocsillation is,a then its time period T is

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`U(x)=k|x|^(3)" "F=(dU)/(dx)=3kx^(2)`
At extreme positons `x=+-a`
`F=maomega^(2)=3Ka^(2)`
`omega prop sqrt(a)" " :. Tprop 1/(sqrt(a))`
Hence `T prop ("amplitude")^(-1//2)`
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