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simple harmonic motion - mass-spring system
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angular speed (omega)
change in theta/change in time
angular speed/angular frequency
2pi radians/T
period
T
frequency
1/T = f
(for mass-spring system) angular frequency
omega = sqrt(k/m)
(for mass-spring system) period
T = 2pi/omega = 2pi(sqrt(m/k))
(for mass-spring system) frequency
f = 1/T = 1/2pi*(sqrt(k/m)) = omega/2pi
phase angle (shift)
phi
position as a function of time
x(t) = A cos ((omega)t + phi)
A
x max
velocity as a function of time
v(t) = -wAsin(w(t)+phi)
-wA
velocity maximum = velocity amplitude
acceleration as a function of time
a(t) = -w²Acos(wt + phi) → -w²(x(t))
-w²A
acceleration max = acceleration amplitude