A particle of mass \( m \) is executing oscillations P about the or...

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A particle of mass \( m \) is executing oscillations
P about the origin on the \( x \)-axis. Its potential energy

W is \( U(x)=k[x]^{3} \), where \( k \) is a positive constant. If the amplitude of oscillation is \( a \), then its time period \( T \) is
(1) Proportional to \( \frac{1}{\sqrt{a}} \)
(2) Independent of \( a \)
(3) Proportional to \( \sqrt{a} \)
(4) Proportional to \( a^{3 / 2} \)
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