# Harmonic Oscillation#

Harmonic Oscillation is a special type of periodic motion where the restoring force $$F$$ on the moving object is directly proportional to the object's displacement magnitude $$x$$ and acts towards the object's equilibrium position. If $$F$$ is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude). If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator.

$F=ma=m{\ddot {x}}=-kx$

Solving this differential equation, we find that the motion is described by the function

$x(t)= A \cdot \cos(2\pi f_0 t - \varphi).$

with the amplitude $$A$$, the frequency $$f_0$$ and the phase shift $$\varphi$$.