Overdamped

Definition

An overdamped system is one in which the damping force is so strong that it prevents oscillations and the system returns to equilibrium without oscillating. The motion is slow and exponential as the system approaches equilibrium.

5 Must Know Facts For Your Next Test

1. In an overdamped system, the damping coefficient $\gamma$ is greater than the critical damping coefficient $\gamma_c$.
2. The characteristic equation has two real and distinct roots in an overdamped system.
3. Overdamping results in a slower return to equilibrium compared to critically damped systems.
4. There are no oscillations in an overdamped response; it simply decays back to equilibrium.
5. Overdamping can be described by the differential equation: $m \ddot{x} + b \dot{x} + kx = 0$, where $b^2 > 4mk$.

Review Questions

• What distinguishes an overdamped system from an underdamped or critically damped system?
• Why does an overdamped system not exhibit oscillations?
• How does the return to equilibrium in an overdamped system compare to a critically damped system?

Related terms

Underdamped:

A system where the damping force is weak enough that it allows for oscillations as it returns to equilibrium.

Critically Damped:

A system where the damping force is just enough to prevent oscillations, allowing it to return to equilibrium in the shortest possible time without oscillating.

Damping Coefficient: $\gamma$, a parameter representing the magnitude of damping in a system. Determines how quickly energy is lost in oscillatory motion.