NEET Sample Paper NEET Sample Test Paper-39

  • question_answer The resultant of two rectangular simple harmonic motions of the same frequency and unequal amplitudes but differing in phase by nil is

    A)  Simple harmonic

    B)  Circular

    C)  Elliptical

    D)  Parabolic

    Correct Answer: C

    Solution :

     If first equation is \[{{y}_{1}}={{a}_{1}}\sin \omega t\] \[\Rightarrow \] \[\sin \,\omega t=\frac{{{y}_{1}}}{{{a}_{1}}}\] ?(i) then second equation will be \[{{y}_{2}}={{a}_{2}}\sin \left( \omega t+\frac{\pi }{2} \right)\] \[={{a}_{2}}\left[ \sin \omega t\cos \frac{\pi }{2}+\cos \omega t\sin \frac{\pi }{2} \right]\] \[={{a}_{2}}\cos \omega t\] \[\Rightarrow \] \[\cos \omega t=\frac{{{y}_{2}}}{{{a}_{2}}}\] ?(ii) By squaring and adding equations (i) and (ii) \[{{\sin }^{2}}\omega t+{{\cos }^{2}}\omega t=\frac{y_{1}^{2}}{a_{1}^{2}}+\frac{y_{2}^{2}}{a_{2}^{2}}\] \[\Rightarrow \]\[\frac{y_{1}^{2}}{a_{1}^{2}}+\frac{y_{2}^{2}}{a_{2}^{2}}=1.\]This is the equation of ellipse.

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