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

  • question_answer
    A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is \[{{E}_{1}}=2J\] and at a displacement y from mean position, its potential energy is\[{{E}_{2}}=8J\]. The potential energy E at a displacement (x + y) from mean position is

    A) 10J      

    B) 14J  

    C) 18J      

    D) 4J

    Correct Answer: C

    Solution :

    [c] \[{{E}_{1}}=\frac{1}{2}k{{x}^{2}},\,{{E}_{2}}=\frac{1}{2}k{{y}^{2}},\] \[E=\frac{1}{2}k{{(x+y)}^{2}}=\frac{1}{2}k{{x}^{2}}+\frac{1}{2}k{{y}^{2}}+kxy\] \[={{E}_{1}}+{{E}_{2}}+2\sqrt{{{E}_{1}}{{E}_{2}}}=2+8+2\sqrt{16}=18J\]


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