Simple harmonic occilations are described by

d2ydt2+ω2y=0\frac{d^2y}{dt^2}+\omega^2y=0

With real solutions on the form

y=Asin⁡(ωt+α)y = A\sin (\omega t + \alpha)

Angular Frequency

ω=2πT=2πf\omega=\frac{2\pi}{T}=2\pi f

Energy for Elastic Pendulum

Wpot=ky22W_{pot} = \frac{ky^2}{2}
Wtot=m2A2ω2W_{tot}=\frac{m}{2}A^2\omega^2
ω=km\omega=\sqrt{\frac{k}{m}}

Wave Number

k=2πλk=\frac{2\pi}{\lambda}