The amplitude of vibration of a particle is given by a m - a 0 a w 2 -bw-c Where a 0 -a-b and c are positive- The condition for a single resultant frequency is

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Question

The amplitude of vibration of a particle is given by $a_{m} = \frac{a_{0}}{a w^{2} - b w + c}$ Where $a_{0}, a, b$ and $c$ are positive. The condition for a single resultant frequency is

b^{2} = 4 a c

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b^{2} > 4 a c

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b^{2} = 5 a c

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b^{2} = 7 a c

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Solution

The correct option is A $b^{2} = 4 a c$
For resonance, amplitude must be maximum which is possible only when the denominator of expression is zero i.e.
$a ω^{2} - b ω + c = 0$

$\Rightarrow ω$ $= \frac{+ b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
For a single resonant frequency, $b = 4 a c$

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The amplitude of vibration of a particle is given by am=a0aw2−bw+c Where a0,a,b and c are positive. The condition for a single resultant frequency is

The correct option is A b2=4acFor resonance, amplitude must be maximum which is possible only when the denominator of expression is zero i.e.aω2−bω+c=0⇒ω =+b±√b2−4ac2aFor a single resonant frequency, b=4ac

The amplitude of vibration of a particle is given by $a_{m} = \frac{a_{0}}{a w^{2} - b w + c}$ Where $a_{0}, a, b$ and $c$ are positive. The condition for a single resultant frequency is

The correct option is A $b^{2} = 4 a c$
For resonance, amplitude must be maximum which is possible only when the denominator of expression is zero i.e.
$a ω^{2} - b ω + c = 0$

$\Rightarrow ω$ $= \frac{+ b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
For a single resonant frequency, $b = 4 a c$