# Equation Blast: Oscillations

While some are contemplating the end of the world, I am studying for physics. Here are the essential oscillations equations to know for our test tomorrow.

**Oscillations (Includes SHM, Springs, Pendulums):**

F=-kx

x_{max}=A

v_{max}=Aw

a_{max}=Aw^{2}

T=1/f and f=1/T

w=angular frequency=2(pi)f=2(pi)/T

v=wr

Potential Energy= (1/2)kA^{2}cos^{2}(wt)

Kinetic Energy= (1/2)kA^{2}sin^{2}(wt)

Total Energy= (1/2)kA^{2}

x(t)= Acos(wt + phase shift)

v(t)= Awsin(wt + phase shift)

a(t)= -Aw^{2}cos(wt + phase shift)

T_{spring}= 2(pi)[m/k]^{1/2}

For use with pendulums only:

T_{pendulum}= 2(pi)[L/g]^{1/2}

w=[(mgL)/(I_{p})]^{1/2}

w=[g/L]^{1/2}

Also, from past units, the torque equations are handy, along with the moment of inertia equations.

STUDY!!!

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