# What is gamma in the damping equation?

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

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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I changed your tag from "harmonic functions" to "differential equations." Harmonic functions are something completely different. – icurays1 Apr 28 '13 at 19:07

$$\sum F = ma$$ In the case of oscillatory systems, such as a spring, there are two forces exerted onto the spring. The restoring force $-kx$ and the damping force $-bv$ where $v$ is the velocity of the spring. Note that the assumption of linear resistive force is only an approximation, and at higher velocities drag is actually proportional to the square of velocity.
\begin{align} -kx-bv &= ma\\ m\ddot{x} + b\dot{x}+kx&=0\\ \ddot{x}+\frac{b}{m}\dot{x}+\frac{k}{m}x &= 0 \end{align} which is the equation you had above.
It's called damping ratio, damping coefficient of damping constant. it measures how the oscillations of the system decay after an initial force is applied. You can calculate it with the expression: $$\gamma=\frac{c}{\sqrt{km}}$$ where $c$ is the friction coefficient, $m$ the mass of the oscillating object and $k$ the elastic constant corresponding to Hooke's law. If $\gamma>1$ we say that the oscillator is overdamped.