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$x''+\gamma x'+w_0^2x=0$

That is the general equation for damped harmonic motion. What is the term or name that describes $\gamma$?

Is it called the damping constant? I know its the ration between the resistive coefficient $b$ and mass of the system $m$ but what do we actually call it ?

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It is common to substitute $\gamma = 2 \zeta \omega_0$. The dimensionless constant $\zeta$ is referred to as the damping ratio. This damping ratio expresses the level of damping relative to critical damping.

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