# 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

Math Solution of Simple Harmonic Oscillation

Math Solution of Simple Harmonic Oscillation