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JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Energy of Simple Harmonic Motion

  • question_answer
    A body is executing Simple Harmonic Motion. At a displacement x its potential energy is \[{{E}_{1}}\] and at a displacement y its potential energy is \[{{E}_{2}}\]. The potential energy E at displacement \[(x+y)\] is  [EAMCET 2001]

    A)            \[\sqrt{E}=\sqrt{{{E}_{1}}}-\sqrt{{{E}_{2}}}\]             

    B)            \[\sqrt{E}=\sqrt{{{E}_{1}}}+\sqrt{{{E}_{2}}}\]

    C)            \[E={{E}_{1}}+{{E}_{2}}\]

    D)            \[E={{E}_{1}}+{{E}_{2}}\]

    Correct Answer: B

    Solution :

                       \[{{E}_{1}}=\frac{1}{2}K{{x}^{2}}\Rightarrow x=\sqrt{\frac{2{{E}_{1}}}{K}}\], \[{{E}_{2}}=\frac{1}{2}K{{y}^{2}}\Rightarrow y=\sqrt{\frac{2{{E}_{2}}}{K}}\]                    and \[E=\frac{1}{2}K{{(x+y)}^{2}}\Rightarrow x+y=\sqrt{\frac{2E}{K}}\]            \[\Rightarrow \sqrt{\frac{2{{E}_{1}}}{K}}+\sqrt{\frac{2{{E}_{2}}}{K}}=\sqrt{\frac{2E}{K}}\]\[\Rightarrow \sqrt{{{E}_{1}}}+\sqrt{{{E}_{2}}}=\sqrt{E}\]


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