Question

Suppose the amplitude of a forced oscillator is given as $x_m=\frac{F_m}{\left[m^2\right({\omega }_d^2-{\omega }^2)+b^2{\omega }_d^2{]}^{\frac{1}{2}}}$ where Fm is the (constant) amplitude of the external oscillating force. At resonance,

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

• A. $\frac{F_m}{b\omega },\frac{F_m}{b{\omega }^2}$
• B. $\frac{F_m}{b{\omega }_d},\frac{F_m}{b}$
• C. $\frac{F_m}{b\omega },\frac{F_m}{b}$
• D. None of these

Answer 1

The correct option is C

$\frac{F_m}{b\omega },\frac{F_m}{b}$

In resonance ${\omega }_d=\omega$ i.e., the driving frequency becomes equal to natural frequency.

So substituting that in the given equation we obtain $X_m=\frac{F}{b\omega }$ and as we know $V_m=\omega X_m=\frac{F}{b}$