[[../02 Areas/Digipen/Mastering Physics|Mastering Physics]] Homework 3 for #digipen/phy250 on [[../02 Areas/Physics/Simple Harmonic Motion|Simple Harmonic Motion]]: ![[../00 Excalidraw/202509271654 .excalidraw.dark.svg]] %%[[../00 Excalidraw/202509271654 .excalidraw.md|🖋 Edit in Excalidraw]], and the [[../00 Excalidraw/202509271654 .excalidraw.light.svg|light exported image]]%% $\huge \begin{align} \cos \theta_{\text{max}} &= \frac{L-\Delta h}{L} \\ L \cos \theta_{\text{max}} &= L - \Delta h \\ \Delta h &= L -L\cos \theta \\ \Delta h &= L(1-\cos \theta) \end{align} $ $ \huge \begin{align} KE_{\text{max}} &=PE_{\text{max}} \\ \frac{1}{2}m v_{\text{max}}^2 &= mg \Delta h \\ \frac{1}{2}m v_{\text{max}}^2 &= mg L(1-\cos\theta) \\ v_{\text{max}}^2 &= 2g L(1-\cos\theta) \\ v_{\text{max}} &= \sqrt{ 2g L(1-\cos\theta) }\\ \end{align} $