Damped Harmonic Oscillator

Harmonic Oscillator where the Force has an extra dampening factor $\lambda$ based on the velocity $v$. We get $F=-kx-\gamma \dot{x}$ . The relevant Equation of motion is $m\ddot{x}+\gamma \dot{x}+kx=0$, and the general solution is $x(t)=a\cos (\omega t)+b\sin (\omega t)$, where

$m\in \mathbb{R}$ is the mass $\gamma \in {\mathbb{R}}^{+}$ is the dampening factor $\omega \in {\mathbb{R}}^{+}$ is the Frequency of Oscillation