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

  • question_answer
    A particle of mass 1 kg is placed in a potential field. Its potential energy is given by \[U=10{{x}^{2}}+5\].The frequency of oscillations of the particle is given by            

    A) \[(\sqrt{10})\]    

    B) \[(\sqrt{5})\]

    C) \[\left( \sqrt{\frac{10}{\pi }} \right)\]        

    D) \[\left( \frac{\sqrt{5}}{\pi } \right)\]

    Correct Answer: D

    Solution :

    [d] \[F=-\frac{dU}{dx}=-20x\] \[a=\frac{F}{M}=\frac{-20x}{1}=-20x\] \[-20x=-{{\omega }^{2}}(x)\] \[\therefore \,\,\,\omega =\sqrt{20}=2\sqrt{5}\] \[f=\frac{\omega }{2\pi }=\frac{2\sqrt{5}}{2\pi }=\left( \frac{\sqrt{5}}{\pi } \right)\]


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