기록

12. Driving Force $ my''+cy'+ky=r(t)=F_{0}cos\omega t $ $ r(t)=F_{0}cos\omega t $: Driving Force $ y=y_{h}+y_{p} $ $ y_{p}=a\cos \omega t+b\sin \omega t $ $ y_{p}'=-\omega a\sin \omega t+\omega b\cos \omega t $ $ y_{p}''=-\omega ^{2}a\cos \omega t-\omega ^{2}b\sin \omega t $ $ \rightarrow m(-\omega ^{2}a\cos \omega t-\omega ^{2}b\sin \omega t)+c(-\omega a\sin \omega t+\omega b\cos \omega t)+k(a\..

6. Free Oscillation of a Mass Spring System - Undamped Small Damping & Short Time → Disregard Damping $ my''+ky=0 $ (k: spring constant) $ y''+\frac{k}{m}y=0 $ $ y''+\omega _{0}^{2}y=0 $ ($ \omega _{0}=\sqrt{\frac{k}{m}} $) $ y=e^{\lambda t} \rightarrow \lambda ^{2}+\omega _{0}^{2}=0 \rightarrow \lambda =\pm \omega _{0}i $ $ \therefore y(t)=A\cos \omega _{0}t+B\sin \omega _{0}t $ $ =\sqrt{A^{2}+..