8.1 Simple Harmonic Motion

The spring-mass system is a SHM because its motion can be described by one single sinusoidal function.

Some of you may be curious why SHM is given such an exotic name. Actually, it comes from mathematicians’ knowledge that any periodic function can be described as a summation of many sinusoidal functions of different frequencies, or harmonics.

Replicate the Fourier transform time-frequency domains ...

For example, the periodical rectangular function (drawn in red) can be constructed by summing five harmonics (drawn in blue). If you want a more perfect rectangular function, more sinusoidal functions of higher frequencies, or higher harmonics are required. If you’re interested, Discrete Fourier Transform is how one can solve for the harmonics of any periodic function.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s