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NEET Sample Paper NEET Sample Test Paper-67

  • question_answer
    Equations \[{{y}_{1}}=A\,\,\sin \,\,\omega t\] and \[{{y}_{2}}\,\,=\,\,\frac{A}{2}\,\sin \,\omega t\,\,+\frac{A}{2}\,\cos \,\,\omega t\] represent S.H.M. The  ratio of the amplitudes of the two motions is

    A) 1         

    B)               2

    C) 0.5                               

    D) \[\sqrt{2}\]

    Correct Answer: D

    Solution :

    \[\,{{y}_{2}}=\frac{A}{2}\,\sin \,\omega t+\frac{A}{2}\,\cos \,\omega t\] \[=\,\,\frac{A}{2}\,(\sin \,\omega t\,\,+\,\,\cos \,\omega t)\] \[=\,\,\frac{A}{2}\,\times \,\,\sqrt{2}\,\,[\sin \,(\omega t\,\,+\,45{}^\circ )]\] \[=\,\,\frac{A}{\sqrt{2}}\,\sin \,(\omega t\,\,+\,45{}^\circ )]\] \[\Rightarrow \,\,\frac{{{A}_{1}}}{{{A}_{2}}}\,\,=\,\,\frac{A}{A/\sqrt{2}}=\sqrt{2}\,\,\]  


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