# Math Solution of Simple Harmonic Oscillation

In mechanics and physics, simple harmonic Oscillation is a type of periodic motion where the restoring force is directly proportional to the displacement. It can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. In addition, other phenomena can be approximated by simple harmonic Oscillation, including the motion of a simple pendulum as well as molecular vibration. Simple harmonic Oscillation is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke’s Law. The motion is sinusoidal in time and demonstrates a single resonant frequency. In order for simple harmonic motion to take place, the net force of the object at the end of the pendulum must be proportional to the displacement.

## Math Solution of Simple Harmonic Oscillation

Simple harmonic motion provides a basis for the characterization of more complicated motions through the techniques of Fourier analysis.

### Math Solution of Simple Harmonic Oscillation

**Math Solution of Simple Harmonic Oscillation**

*Math Solution of Simple Harmonic Oscillation*

Math Solution of Simple Harmonic Oscillation

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Math Solution of Simple Harmonic Oscillation

Math Solution of Simple Harmonic Oscillation