JEE Main & Advanced Physics Simple Harmonic Motion Question Bank Assertion and Reason

  • question_answer
    Assertion             :       Resonance is special case of forced vibration in which the natural frequency of vibration of the body is the same as the impressed frequency of external periodic force and the amplitude of forced vibration is maximum.  Reason                 :       The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force. [AIIMS 1994]

    A)             If both assertion and reason are true and the reason is the correct explanation of the assertion.

    B)             If both assertion and reason are true but reason is not the correct explanation of the assertion.

    C)             If assertion is true but reason is false.

    D)             If the assertion and reason both are false.

    E)             If assertion is false but reason is true.

    Correct Answer: C

    Solution :

                       Amplitude of oscillation for a forced, damped oscillator is  \[A=\frac{{{F}_{0}}/m}{\sqrt{({{\omega }^{2}}-\omega _{0}^{2})+{{(b\omega /m)}^{2}}}},\]where b is constant related to the strength of the resistive force, \[{{\omega }_{0}}=\sqrt{k/m}\] is natural frequency of undamped oscillator (b = 0). When the frequency of driving force (w) » \[{{\omega }_{0}}\], then amplitude A is very larger. For w < w0 or w > w0, the amplitude decrease.


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