# Simple Harmonic Motion

1. Nov 4, 2009

### Kev1n

1. Angular frequency is introduced into the analysis of simple harmonic motion because:

1. Because the unit of hz is not a convnient unit for frquency. 2. to create a mathematical relationship between displacement and time. 3. To create a link between mass and frequency of vibration. 4. Because vibration is naturally circular

3. I think 4. Naturally circular

2. Nov 4, 2009

### Andrew Mason

Try 2. The reason angular frequency is used in simple harmonic motion is mathematical - SHM is described mathematically by a sinusoidal function. The general solution to the differential equation:

$$\ddot s = - ks$$

is a sin wave $s = Asin(\omega t + \phi)$ So the position, s, varies with time exactly the same way that the sin of the angle varies when something undergoes uniform circular motion.

AM

3. Nov 4, 2009