For a simple oscillator consisting of a mass m to one end of a spring with a spring constant s, the restoring force, f, can be expressed by the equation
where displacement is the displacement of the mass from its rest position. Substituting the expression for f into the linear momentum equation,
where a is the acceleration of the mass, we can get
To solve the equation, we can assume
The general solution for this type of 'simple harmonic motion' is x=Asin(wt+phi). Here, phi(the angle expressed in radians) is known as the phase of the simple harmonic motion.