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EAMCET Medical EAMCET Medical Solved Paper-2004

  • question_answer
    The equation of motion of a particle executing SHM is, \[\alpha +16{{\pi }^{2}}x=0.\]In this equation \[\alpha \] is the linear acceleration in \[m/{{s}^{2}},\]of the particle at a displacement x metre. The time period of SHM, in second, is:

    A)                  \[\frac{1}{4}\]                                                  

    B)                  \[\frac{1}{2}\]

    C)                  1                                            

    D)                  2

    Correct Answer: B

    Solution :

                     The equation of motion and particles executing SHM is given by                 \[\alpha +16{{\pi }^{2}}x=0\]                 \[\alpha =-16{{\pi }^{2}}x\]                 But from the relation in SHM, acceleration is given by                 \[\alpha =-{{\omega }^{2}}x\]                 So,                          \[-{{\omega }^{2}}x=-16{{\pi }^{2}}x\]                 or                            \[\omega =4\pi \]            \[\,\,\,(\because \omega =2\frac{\pi }{T})\]                 or                            \[\frac{2\pi }{T}=4\pi \]                 Hence,                  \[T=\frac{1}{2}s\]


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