Example Problem for a [[../02 Areas/Physics/Damped Harmonic Oscillators|Damped Harmonic Oscillator]] There is a sign being dragged by the wind: ![[../00 Excalidraw/202509261357 .excalidraw]] Lets say we know the wind blew the sign $5\degree$, and the wind speed is $10 \op{\frac{m}{s}}$. $ \begin{align} \vec D &=-bV \\ \vec W &= mg \\ \end{align}$ $\begin{align} mg \sin \theta &\approx bV \\ b &\approx \frac{mg\theta}{V} = mg \frac{5 \degree}{10 \pu{ ms-1 } } \\ \frac{b}{2m} &= \frac{g 5 \degree}{2\cdot 10 \pu{ ms-1 }} \\ g &\approx 10 \pu{ ms-1 }\\ \frac{b}{2m} &=\frac{5\degree}{2} \pu{ deg/s } \\ x(t) &= 5\degree e^{- \frac{5\degree}{2}t } \sin\pa{ \sqrt{ \frac{g}{l} }t + \frac{\pi}{2} } \end{align}$