SHM Hooke's Law connections
Not derived in lectures or book

 As shown below the frequency and period of the wave description for an object undergoing simple harmonic motion can be calculated from the mass of the object and the force constant in Hooke's law.

	ω = √  k    f = 1  √  k    T = 2π √  m  m  2π m k The spring bobs up and down more frequently if the spring is stiffer (k larger) less frequently if the object is heavier (mass (m) is larger)
from wikipedia.com, Simple harmonic oscillator	The following describes how these relationships can be derived. Displacement as a function of time.  x = X cos ωt (1) Velocity is the derivative of distance with respect to time:   vx = dx = d (X cos ωt) dt dt vx = – Xω sin (ωt) (2) Acceleration is the derivative of velocity with respect to time: ax = dv = d (–Xω sin ωt) dt dt
Hooke's Law F = -kx k force constant of the spring x the displacement  F = ma ax = – k x m	ax = –Xω2 cos (ωt) (3) ax =  –ω2 × Xcos ωt Substitution from equation (1) ax = –ω2x (4) Substituting from Hooke's Law and rearranging to solve for ω results in the relationships shown below between the force constant (k), the mass of the oscillating object and the properties of the wave. – ω2x = – k x m   ω = √  k  m The other relationships above are then derived from this using the relationship between angular frequency, frequency and period.