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Exercise · Q17

Q.What is resonance? Explain, in qualitative terms, why the amplitude of a forced oscillation becomes very large when the driving frequency is close to the natural frequency of the system. Give two everyday examples of resonance.

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Resonance is the special case of forced oscillation in which the driving frequency ωd\omega_d is equal to, or very nearly equal to, the system's own natural frequency ω0\omega_0.

In an ordinary forced oscillation with ωd\omega_d far from ω0\omega_0, the external force and the system's own natural motion are not synchronised, so over successive cycles the force sometimes adds energy to the motion and sometimes removes it, and only a modest steady amplitude builds up. But when ωd=ω0\omega_d=\omega_0, the external force arrives in step with the system's own natural rhythm at every single cycle -- pushing in the same direction the system is already moving, at exactly the right moments -- so it keeps adding energy to the oscillation in exactly the right phase, cycle after cycle, without ever working against the motion. As a result, the amplitude of oscillation grows to a value far larger than the same force could produce at any other driving frequency (limited only by whatever damping is present in the real system). …

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