Simple Harmonic Motion (SHM) is really important when we talk about how waves act. Both SHM and waves show a special kind of repeating motion.

Connection: We can think about SHM as a kind of wave called a harmonic wave.

Here's a simple way to show it:

$$y(x, t) = A \cos(kx - \omega t + \phi)$$

In this formula:

• A is the amplitude, or how high the wave goes.
• k is the wave number, which tells us how many waves fit in a space.
• ω is the angular frequency, which shows how fast the wave moves.

Fourier Analysis: This is a method that takes complicated waves and breaks them down into simpler parts made of SHM. This helps us understand wave shapes better.

Applications: SHM is used in many areas like sound, light, and electrical engineering. It plays a big role in fields such as communication and medicine.