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

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A particle of mass \( m \) is executing oscillations about the origin on the \( x \)-axis. Its potential energy is \( U(x)=k|x|^{3} \),
\( \mathrm{P} \) where \( k \) is a positive constant. If the amplitude of oscillation is \( A \), then its time period \( T \) is [IIT-JEE 1998; AIIMS 2008]
W
(a) Proportional to \( \frac{1}{\sqrt{A}} \)
(b) Independent of \( A \)
(c) Proportional to \( \sqrt{A} \)
(d) Proportional to \( A^{3 / 2} \)
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