Definition:Overdamped
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Definition
Consider a physical system $S$ whose behaviour can be described with the second order ODE in the form:
- $(1): \quad \dfrac {\d^2 x} {\d t^2} + 2 b \dfrac {\d x} {\d t} + a^2 x = 0$
for $a, b \in \R_{>0}$.
Let $b > a$, so that the solution of $(1)$ is in the form:
- $x = C_1 e^{m_1 t} + C_2 e^{m_1 t}$
for $m_1, m_2 < 0$.
Then $S$ is described as being overdamped.
Also known as
An overdamped system is also known as heavily damped, or undergoing heavy damping.
Also see
Sources
- 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.20$: Vibrations in Mechanical Systems
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): damped harmonic motion
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): damped harmonic motion