$Assertion :$ Resonance is a 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.
$Reason :$ The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force.
AIIMS 2010, Medium
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The amplitude become large when the frequency of the driving force $(\omega)$ is near the natural frequency of oscillation or when
$\omega=\omega_{0} .$ This frequency is known as resonance frequency. Amplitude of oscillation for a forced, damped oscillator is
$A=\frac{F_{0} / m}{\sqrt{\left(\omega^{2}-\omega_{0}^{2}\right)+(b \omega / m)^{2}}}$
where $b$ is constant related to the strength
of the resistive force, $\omega_{0}=\sqrt{k / m}$ is natural frequency of undamped oscillator$(b=0)$.
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