If the amplitude of velocity of a particle acted by a force F - F 0cos- t along x-axis is given byv 0-1- a -2- b - c 1-2- where b 2-4 acThe frequency of resonance is -A- -b-aB- b -2 aC- a-bD- a -2 b

The correct option is B b/2a For resonance v_0 →∞ (max) ∴ (a ω^2 b ω + c) = 0 or d/d ω (a ω^2 b ω + c) = 0 or 2a ω b = 0 or ω = b/2a ...

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Byju's Answer

Standard XII

Physics

Properties of Field Lines

If the amplit...

Question

If the amplitude of velocity of a particle acted by a force
$F = F_{0} c o s ω t$ along x-axis is given by
$v_{0} = \frac{1}{(a ω^{2} - b ω + c)^{\frac{1}{2}}}, w h e r e b^{2} > 4 a c$
The frequency of resonance is :

$ω = \frac{b}{a}$

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$\frac{b}{2 a}$

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$\frac{a}{b}$

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$\frac{a}{2 b}$

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Solution

The correct option is B
$\frac{b}{2 a}$

For resonance $v_{0} \to \infty (m a x)$

$∴ (a ω^{2} - b ω + c) = 0$

or $\frac{d}{d ω} (a ω^{2} - b ω + c) = 0$

or $2 a ω - b = 0 o r ω = \frac{b}{2 a}$

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If the amplitude of velocity of a particle acted by a force F=F0cosωt along x-axis is given by v0=1(aω2−bω+c)12, where b2>4ac The frequency of resonance is :

The correct option is B b2a For resonance v0→∞ (max) ∴(aω2−bω+c)=0 or ddω(aω2−bω+c)=0 or 2aω−b=0 or ω=b2a

If the amplitude of velocity of a particle acted by a force
$F = F_{0} c o s ω t$ along x-axis is given by
$v_{0} = \frac{1}{(a ω^{2} - b ω + c)^{\frac{1}{2}}}, w h e r e b^{2} > 4 a c$
The frequency of resonance is :

The correct option is B
$\frac{b}{2 a}$

For resonance $v_{0} \to \infty (m a x)$

$∴ (a ω^{2} - b ω + c) = 0$

or $\frac{d}{d ω} (a ω^{2} - b ω + c) = 0$

or $2 a ω - b = 0 o r ω = \frac{b}{2 a}$