Underdamped

Definition

An underdamped system is one where the damping force is not strong enough to prevent oscillations. The system will oscillate with a gradually decreasing amplitude over time.

5 Must Know Facts For Your Next Test

1. In an underdamped system, the damping coefficient $\gamma$ is less than twice the natural frequency $\omega_0$ ($\gamma < 2\omega_0$).
2. The system exhibits oscillatory motion with an exponentially decaying amplitude.
3. The frequency of oscillation in an underdamped system is called the damped natural frequency and is less than the undamped natural frequency.
4. The mathematical solution for displacement in an underdamped system involves both sinusoidal functions and exponential decay terms.
5. Underdamping can be observed in various physical systems such as RLC circuits, mechanical springs, and pendulums with air resistance.

Review Questions

• What condition must be met for a harmonic oscillator to be considered underdamped?
• Explain how the amplitude of an underdamped oscillator changes over time.
• How does the damped natural frequency compare to the undamped natural frequency in an underdamped system?

Related terms

Damping Coefficient: A parameter representing the amount of damping in a system, usually denoted by $\gamma$. It affects how quickly energy is lost from the system.

Critical Damping: Occurs when the damping coefficient is equal to twice the natural frequency ($\gamma = 2\omega_0$), resulting in no oscillations and fastest return to equilibrium.

Overdamping: $\gamma > 2\omega_0$, causing a system to return to equilibrium without oscillating but more slowly than in critical damping.