Overdamped

Definition

Overdamped describes a system where the damping force is so strong that it prevents oscillations and the system returns to equilibrium without oscillating. This occurs when the damping coefficient is greater than the critical damping coefficient.

5 Must Know Facts For Your Next Test

1. In an overdamped system, the damping constant $b$ is greater than $2\sqrt{mk}$, where $m$ is mass and $k$ is the spring constant.
2. Overdamping results in a slow return to equilibrium without any oscillation.
3. The characteristic equation of an overdamped harmonic oscillator has two distinct real roots.
4. An overdamped response takes longer to reach equilibrium compared to a critically damped response but avoids oscillations entirely.
5. Examples of overdamped systems include some automotive shock absorbers and certain electrical circuits.

Review Questions

• What condition must be met for a system to be considered overdamped?
• How does an overdamped system behave when displaced from its equilibrium position?
• Compare and contrast the time it takes for an overdamped system to return to equilibrium with that of a critically damped system.

Related terms

Critically Damped:

A state where the damping force allows the system to return to equilibrium as quickly as possible without oscillating.

Underdamped:

A state where the damping force is weak enough that the system oscillates while gradually returning to equilibrium.

\text{Damping Coefficient}: $b$, a parameter representing the amount of damping in a system, influencing whether it is underdamped, critically damped, or overdamped.