High School Physics/Simple Oscillation

< High School Physics

Simple OscillationEdit

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

 


or,

 


Note that

 


To solve the equation, we can assume

 

The general solution for this type of 'simple harmonic motion' is  . Here,   (the angle expressed in radians) is known as the phase of the simple harmonic motion.