Damped oscillations Quiz

1. $x''+4x'+13x=0$. What type of damping is this?

• A. Critical
• B. Heavy
• C. Light
• D. None

2. $x''+8x'+16x=0$ has general solution:

• A. $Ae^{-4t}+Be^{4t}$
• B. $(A+Bt)e^{-4t}$
• C. $e^{-4t}(A\cos4t+B\sin4t)$
• D. $Ae^{-8t}+Be^{-2t}$

3. A particle has $x''+kx'+25x=0$. For which $k$ is the damping critical?

• A. $k=5$
• B. $k=25$
• C. $k=10$
• D. $k=\frac{25}{2}$

4. $x''+5x'+4x=0$. Which describes the motion?

• A. Oscillation with decaying amplitude
• B. No oscillation, slow return to $O$
• C. Fastest return, repeated root
• D. Simple harmonic motion

5. In light damping $x=e^{-2t}(A\cos3t+B\sin3t)$. What is the time between successive maxima?

• A. $\frac{3}{2\pi}$ s
• B. $\frac{2\pi}{3}$ s
• C. $\frac{\pi}{2}$ s
• D. $2\pi$ s