Final Exam Equations

Drag

Notice that $\frac{dv}{dt}=\text{acceleration}$ so $M\frac{dv}{dt}=F(F=ma)$

Spring-Mass Systems

Unforced Vibrations

Undamped vibrations: $m\frac{d^{2}y}{d{t}^2}+\omega \frac{dy}{dt}+ky=0$

Overdamped if ${\omega }^2>4km$

Critical Damped if ${\omega }^2=4km$

Underdamped if ${\omega }^2<4km$

Undamped if $\omega =0$

Period $T=\frac{2\pi }{\omega }$

$f=\frac{\omega }{2\pi }$ is frequency in hertz

Forced Vibrations

$\frac{d^{2}y}{d{t}^2}={\omega }^{2}y=f_{a}cos(\omega t)$

$\omega =\sqrt{\frac{k}{m}}$ is the resonant natural frequency