Critical damping

Definition

Critical damping occurs when a damping force is applied to an oscillating system, bringing it to rest in the shortest possible time without oscillation. It represents the threshold between overdamping and underdamping.

5 Must Know Facts For Your Next Test

1. In critically damped systems, the damping coefficient $\zeta$ is equal to 1.
2. Critically damped systems return to equilibrium as quickly as possible without oscillating.
3. The general solution for a critically damped oscillator involves terms that decay exponentially with time.
4. Practical applications of critical damping include shock absorbers in vehicles and door closers.
5. Critical damping ensures that the system does not overshoot its equilibrium position.

Review Questions

• What is the value of the damping coefficient $\zeta$ for a critically damped system?
• How does critical damping affect the return to equilibrium compared to underdamping and overdamping?
• Give an example of a real-world application where critical damping is desirable.

Related terms

Underdamping: Occurs when the damping force is not strong enough to prevent oscillations but still reduces their amplitude over time.

Overdamping: Occurs when the damping force is so strong that it prevents oscillations and causes the system to return slowly to equilibrium.

Damping Coefficient: $\zeta$; A dimensionless measure indicating how much damping affects an oscillating system, with values indicating underdamped ($\zeta < 1$), critically damped ($\zeta = 1$), or overdamped ($\zeta > 1$) conditions.