2. Waves and Oscillations

Damped Oscillations — Quiz

Test your understanding of damped oscillations with 5 practice questions.

Practice Questions

Question 1

Which damping regime yields the quickest return to equilibrium without oscillation?

Question 2

A mass–spring–damper system has mass $m=2.00\,\mathrm{kg}$, spring constant $k=18.0\,\mathrm{N/m}$, and damping coefficient $b=12.0\,\mathrm{N\cdot s/m}$. Calculate the damping ratio $\zeta$ and identify the regime.

Question 3

If the amplitude envelope of a damped oscillator is $A(t)=A_0e^{-\gamma t}$ and the amplitude falls to 10% of its initial value in $t=5.0\,\mathrm{s}$, what is the decay constant $\gamma$?

Question 4

For an underdamped oscillator, the damped natural angular frequency $\omega_{d}$ is given by $\omega_{d}=\omega_{0}\sqrt{1-\zeta^2}$. If $\omega_{0}=10.0\,\mathrm{rad/s}$ and $\zeta=0.20$, what is $\omega_{d}$?

Question 5

What is the general solution for the displacement $x(t)$ of a critically damped oscillator with natural frequency $\omega_{0}$?