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

b²=4ac

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

b²>4ac

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

b²=5ac

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

b²=7ac

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

Open in App

Solution

The correct option is A
b²=4ac

For resonance amplitude must be maximum which is possible onlu.

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 , $b^{2} = 4 a c$ .

Suggest Corrections

Similar questions

Q. 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

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 :

Q. The displacement of a particle executing simple harmonic motion is given by

y = A_{0} + A sin ω t + B cos ω t

. Then, the amplitude of its oscillation is given by

Q. Given that the roots of the equation

a x^{2} + b x + c = 0

are the consecutive terms of an A.P.What is the common difference of the A.P. in terms of a, b and c?

Q. Discriminant of the equation

a x^{2} + b x + c = 0

is given by

Join BYJU'S Learning Program

The amplitude of vibration of a particle is given by am=(a0)(aω2−bω+c) where a0,a,b and c are positive. The condition for a single resonant frequency is

The correct option is A b2=4ac For resonance amplitude must be maximum which is possible onlu. When the denominator of expression is zero i.e. aω2−bω+c=0⇒ω=+b±√b2−4ac2a For a single resonant frequency , b2=4ac .

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

The correct option is A
b²=4ac

For resonance amplitude must be maximum which is possible onlu.

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 , $b^{2} = 4 a c$ .