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AFMC AFMC Solved Paper-2001

  • question_answer
    Two panicles are excuting simple harmonic motion. At an instant of lime t their displacements are \[{{Y}_{1}}=\alpha \cos (\omega t)\] and \[{{Y}_{2}}=\alpha \sin (\omega t)\] Then the phase difference between.\[{{Y}_{1}}\] and \[{{Y}_{2}}\] is:

    A) \[120{}^\circ\]

    B) \[90{}^\circ\]

    C) \[180{}^\circ\]                        

    D) zero

    Correct Answer: B

    Solution :

    Key Idea: Cosine expression can be expressed in terms of sine expression using identity  \[\sin (\pi /2+\theta )=cos\theta .\] The given displacement equations are \[{{y}_{1}}=a\cos \omega t\] \[{{y}_{1}}=a\sin \left( \omega t+\frac{\pi }{2} \right)\] ?(i) and    \[{{y}_{2}}=a\sin \omega t\] Hence, phase difference between \[{{y}_{1}}\]and \[{{y}_{2}}\] Hence, phase difference is \[{{90}^{o}}.\]


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