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Asked: 2022-11-06T14:21:56+05:30 In:

Why vibration amplitude is high at resonance frequency?

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Why does amplitude increase at resonance?  How does resonance affect amplitude? Is amplitude maximum at resonance?

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    1. Consider a spring mass system subjected to harmonic force of magnitude F= F_0 sin(\omega t) \, as shown in the figure below.

      Where  F_0 \,represents the maximum amplitude of applied force.

      /omega \,represents the frequency of applied force.

      The response of a system is given by following equations.

      The rate of energy transfer to the system is given by the product of Force applied and velocity of the system.

      Rate of energy transfer to the system = \overrightarrow{F}. \overrightarrow{V}

      Since it is a dot product, the rate of energy transfer is maximum when the force vector and velocity vector is in-phase. At resonant condition, the direction of applied force and the direction of velocity of the system is same.

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