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 ?
 A: 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.
A: The second order differential equation arises from the application of Newton's Second Law.
$$\sum F = ma$$
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.
