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Simple Harmonic Motion
Velocity and Acceleration
Practice Problems
SHM Overview
Additional Links

While finding the displacement is important, it is also necessary to be able to find the velocity of a simple harmonic oscillator as a specific point in time.
Velocity is related to displacement in the sense that it is its derivative (the slope of a displacement vs. time graph's tangent line at a particular time).
** Overlooking rather tedius and unimportant derivations **
v(t) = -Aωcos(ωt)
Where:  v(t) = the velocity at time, t (s)
               A = the maximum displacement (m)
               ω = angular acceleration = 2πf = 2π/T (rad/s) 

Acceleration is related to velocity in the same way.
** More unimportant derivations **
a(t) = -Aw2cos(ωt)
Where:  a(t) = the acceleration at time, t (m/s2)

Alesa Rabson & Maria Forero - Simple Harmonic Motion