How is simple harmonic motion related to wave motion?

Simple harmonic motion is a type of periodic motion that is related to wave motion.

Simple harmonic motion (SHM) is a type of motion where the restoring force is proportional to the displacement from equilibrium. This type of motion is seen in systems such as a mass on a spring or a pendulum. SHM can be described mathematically using sine and cosine functions, which are also used to describe wave motion.

Wave motion is the transfer of energy through a medium without the transfer of matter. Waves can be described by their amplitude, wavelength, frequency and speed. The motion of particles in a wave is also periodic, similar to SHM. The motion of particles in a wave is perpendicular to the direction of the wave, whereas in SHM the motion is along a single axis.

The relationship between SHM and wave motion can be seen in the example of a vibrating string. When a string is plucked, it undergoes SHM, with the restoring force provided by tension in the string. This motion creates a disturbance in the string, which travels along the length of the string as a wave. The wave can be described by its amplitude, wavelength, frequency and speed, just like any other wave.

In conclusion, SHM and wave motion are related through their periodic nature and the use of sine and cosine functions to describe their motion. The motion of particles in a wave is perpendicular to the direction of the wave, whereas in SHM the motion is along a single axis.