6. Nonhomogeneous Linear Equations

Mechanical Applications — Quiz

Test your understanding of mechanical applications with 5 practice questions.

Practice Questions

Question 1

Which differential equation correctly models a forced mass-spring-damper system with mass $m$, damping coefficient $c$, spring constant $k$, displacement $x(t)$, and external force $F(t)$?

Question 2

In the model $m x'' + c x' + kx = F(t)$, what physical effect does the term $c x'$ represent?

Question 3

A spring has spring constant $k=20\text{ N/m}$ and is attached to a mass $m=5\text{ kg}$ with no damping. What is the natural angular frequency of the system?

Question 4

For the undamped, unforced system $2x''+18x=0$, what is the natural angular frequency?

Question 5

For an underdamped system modeled by $m x'' + c x' + kx = 0$ with $c>0$, what happens to the oscillations over time?