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JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    A SHM of a 2g mass is defined by \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+0.2\frac{dy}{dt}+36y=0\]. Then the time period and quality factor Q are respectively:

    A)  \[\frac{\pi }{3}s,\,30\]                  

    B)  \[\frac{\pi }{2},\,s,20\]

    C)  \[\pi \,s,\,10\]                 

    D)  \[2\pi s,\,10\]

    Correct Answer: A

    Solution :

    Since a SHM is defined as \[\frac{{{d}^{2}}y}{d{{t}^{2}}}+0.2\frac{dy}{dt}=-{{\omega }^{2}}y,\] we have \[{{\omega }^{2}}=36\] \[\Rightarrow \,\,\omega =6\] \[\Rightarrow \,\,t=\frac{\pi }{3}\sec \] \[Q.\,\text{factor}=\frac{\omega }{\text{coefficient}\,\text{of}\,\frac{dy}{dt}}=\frac{6}{0.2}=30\]


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