Suppose the amplitude of a forced oscillator is given as $x_{m} = \frac{F_{m}}{[m^{2} (ω_{d}^{2} - ω^{2}) + b^{2} ω_{d}^{2}]^{\frac{1}{2}}}$ where Fm is the (constant) amplitude of the external oscillating force. At resonance,

what are the amplitude and velocity amplitude of the oscillating object?

$\frac{F_{m}}{b ω}, \frac{F_{m}}{b ω^{2}}$

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

$\frac{F_{m}}{b ω_{d}}, \frac{F_{m}}{b}$

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

$\frac{F_{m}}{b ω}, \frac{F_{m}}{b}$

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

None of these

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

Open in App

Solution

The correct option is C
$\frac{F_{m}}{b ω}, \frac{F_{m}}{b}$

In resonance $ω_{d} = ω$ i.e., the driving frequency becomes equal to natural frequency.

So substituting that in the given equation we obtain $X_{m} = \frac{F}{b ω}$ and as we know $V_{m} = ω X_{m} = \frac{F}{b}$

Suggest Corrections

Similar questions

Suppose the amplitude of a forced oscillator is given as $x_{m} = \frac{F_{m}}{[m^{2} (ω_{d}^{2} - ω^{2}) + b^{2} ω_{d}^{2}]^{\frac{1}{2}}}$ where Fm is the (constant) amplitude of the external oscillating force. At resonance,

what are the amplitude and velocity amplitude of the oscillating object?

Q. At resonance, the amplitude of forced oscillations 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. In the case of sustained forced oscillations the amplitude of oscillations,

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

Join BYJU'S Learning Program

Suppose the amplitude of a forced oscillator is given as xm=Fm[m2(ω2d−ω2)+b2ω2d]12 where Fm is the (constant) amplitude of the external oscillating force. At resonance, what are the amplitude and velocity amplitude of the oscillating object?

The correct option is C Fmbω,Fmb In resonance ωd=ω i.e., the driving frequency becomes equal to natural frequency. So substituting that in the given equation we obtain Xm=Fbω and as we know Vm=ω Xm=Fb

The correct option is C
$\frac{F_{m}}{b ω}, \frac{F_{m}}{b}$

In resonance $ω_{d} = ω$ i.e., the driving frequency becomes equal to natural frequency.

So substituting that in the given equation we obtain $X_{m} = \frac{F}{b ω}$ and as we know $V_{m} = ω X_{m} = \frac{F}{b}$