1.

A particle of mass m oscillates with a potential energy\[U={{U}_{0}}+\alpha \,\,{{x}^{2}}\], where \[{{U}_{0}}\] and a are constants and x is the displacement of particle from equilibrium position. The time period of oscillation is

A. \[2\pi \sqrt{\frac{m}{\alpha }}\]
B. \[2\pi \sqrt{\frac{m}{2\alpha }}\]
C. \[\pi \sqrt{\frac{2m}{\alpha }}\]
D. \[2\pi \sqrt{\frac{m}{{{\alpha }^{2}}}}\]
Answer» C. \[\pi \sqrt{\frac{2m}{\alpha }}\]


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