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JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Critical Thinking

  • question_answer
    The amplitude of vibration of a particle is given by \[{{a}_{m}}=({{a}_{0}})/(a{{\omega }^{2}}-b\omega +c);\] where \[{{a}_{0}},a,b\] and c are positive. The condition for a single resonant frequency is [CPMT 1982]

    A)            \[{{b}^{2}}=4ac\]                

    B)            \[{{b}^{2}}>4ac\]

    C)            \[{{b}^{2}}=5ac\]                

    D)            \[{{b}^{2}}=7ac\]

    Correct Answer: A

    Solution :

                       For resonance amplitude must be maximum which is possible only when the denominator of expression is zero i.e. \[a{{\omega }^{2}}-b\omega +c=0\] \[\Rightarrow \omega =\frac{+b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] For a single resonant frequency, b2 = 4ac.


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