Damped Oscillations Quiz with Answer Key

📚 Quick Study Guide

🔍 Damped Oscillation: Oscillation where energy dissipates over time, causing amplitude to decrease. 📉 Damping Force: A force that opposes motion and causes damping (e.g., friction, air resistance). ➗ Damping Coefficient (b): Represents the strength of the damping force. ➗ Underdamped: System oscillates with gradually decreasing amplitude. ($b < 2\sqrt{mk}$) ➗ Critically Damped: System returns to equilibrium as quickly as possible without oscillating. ($b = 2\sqrt{mk}$) ➗ Overdamped: System returns to equilibrium slowly without oscillating. ($b > 2\sqrt{mk}$) ➗ Equation of Motion: $m\frac{d^2x}{dt^2} + b\frac{dx}{dt} + kx = 0$, where $m$ is mass, $b$ is the damping coefficient, and $k$ is the spring constant.

🧪 Practice Quiz

1. Which of the following is the primary cause of damped oscillations?
   1. External force applied to the system
   2. Conservation of energy
   3. Energy dissipation due to friction
   4. Increase in potential energy
2. In an underdamped system, what type of motion is observed?
   1. Motion with constant amplitude
   2. Motion with exponentially increasing amplitude
   3. Oscillatory motion with decreasing amplitude
   4. No motion at all
3. What happens to the frequency of oscillation as damping increases (but the system remains underdamped)?
   1. The frequency increases.
   2. The frequency decreases.
   3. The frequency remains constant.
   4. The frequency becomes zero.
4. In a critically damped system, how does the system return to equilibrium?
   1. Slowly with oscillations
   2. Quickly without oscillations
   3. Slowly without oscillations
   4. Instantly with large oscillations
5. Which parameter determines the degree of damping in an oscillatory system?
   1. Mass of the object
   2. Spring constant
   3. Damping coefficient
   4. Gravitational acceleration
6. What is the effect of overdamping on the return to equilibrium?
   1. Fast return with oscillations
   2. Fast return without oscillations
   3. Slow return with oscillations
   4. Slow return without oscillations
7. A damped oscillator's amplitude decreases to half its initial value in 10 seconds. What happens to its energy?
   1. It halves in 10 seconds.
   2. It reduces to one-fourth in 10 seconds.
   3. It remains the same.
   4. It becomes zero.