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

Question

Dr. Abubacker · Accepted Answer

(a) For resonance amplitude must be maximum which is possible only when the denominator of expansion 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, $b^{2} = 4ac$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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