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JEE Main & Advanced Physics Wave Mechanics Question Bank Self Evaluation Test - Oscillations

  • question_answer
    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) \[2\pi \sqrt{\frac{m}{{{\alpha }^{2}}}}\]

    Correct Answer: B

    Solution :

    [b] \[U={{U}_{0}}+\alpha {{x}^{2}}\Rightarrow F=-\frac{DU}{dx}=-2\alpha x\] \[a=\frac{F}{m}=-\frac{2\alpha }{m}x\] \[\Rightarrow \,\,{{\omega }^{2}}=\frac{2\alpha }{m}\Rightarrow T=\frac{2\pi }{\omega }\Rightarrow T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{m}{2\alpha }}\]


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