High School Physics/Simple Oscillation

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Simple Oscillation[edit]

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.