# Harmonic Oscillator

## A simple harmonic oscillator

A simple harmonic motion can be used as a mathematical model for a variety of motions such as the oscillation of a spring.

The time period of a simple harmonic oscillator can be expressed as

*T = 2 π (m / k) ^{1/2 } (1)^{}*

*where *

*T = time period (s)*

*m = mass (kg) *

*k = spring constant (N/m)*

### Example - Time Period of a Simple Harmonic Oscillator

A mass of *500 kg* is connected to a spring with a spring constant *16000 N/m*. The time period can be calculated as

*T = 2 π ((500 kg) / (16000 N/m)) ^{1/2 }*

* = 1.1 s*