2. Waves and Oscillations

Forced Resonance — Quiz

Test your understanding of forced resonance with 5 practice questions.

Practice Questions

Question 1

Which statement about the resonant angular frequency $\omega_r$ in a lightly damped oscillator is correct?

Question 2

A mass-spring oscillator has mass $m=0.5\,\mathrm{kg}$, spring constant $k=200\,\mathrm{N/m}$, and damping coefficient $b=4.0\,\mathrm{kg/s}$. Calculate its resonant angular frequency $\omega_r$ using $\omega_r\approx\sqrt{\omega_0^2 - (\tfrac{b}{m})^2/2}$.

Question 3

In a driven damped oscillator with mass $m$, damping coefficient $b$, spring constant $k$, and driving force amplitude $F_0$, the steady-state amplitude at resonance is $A_{\max}=\frac{F_0}{b\,\omega_0}$. For $F_0=10\,\mathrm{N}$, $b=2.0\,\mathrm{kg/s}$, $m=1.0\,\mathrm{kg}$, and $k=50\,\mathrm{N/m}$, compute $A_{\max}$.

Question 4

How does increasing the damping coefficient $b$ affect the amplitude response curve of a driven oscillator?

Question 5

Under which condition would beats be observed in a driven oscillator?