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 ...

You visited us 2 times! Enjoying our articles? Unlock Full Access!

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 :

$ω = \frac{b}{a}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{b}{2 a}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{a}{b}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{a}{2 b}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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

Suggest Corrections

Similar questions

Q. A driven oscillator is acted upon by a force

F = F_{0} s i n ω

. The amplitude of oscillation is given by

A = \frac{F_{0}}{\sqrt{a ω^{2} - b ω + c}}

, the resonant angular frequency is

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

Q. A forced oscillator is acted upon by a force

F = F_{\circ} s i n ω t .

. The amplitude of oscillation is given by

\frac{55}{\sqrt{2 ω^{2} - 36 ω + 9}}

. The resonant angular frequency is

Q. If

x = a + b, y = a ω + b ω^{2}, z = a ω^{2} + b ω

, then xyz equals to where,

ω

is the cube root of unity.

Q. The speed

v

of a particle moving along x-axis is given by,

v^{2} = 8 b x - x^{2} - 12 b^{2},

where b is a constant. Find amplitude of oscillations. (b = 2 units)

Join BYJU'S Learning Program

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