Periodic motion refers to any type of motion that repeats itself at regular intervals. This can be seen in a variety of natural phenomena, such as the changing of seasons, the swinging of a pendulum, or the vibrations of a guitar string.
Simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position. In other words, the motion follows a sinusoidal pattern. However, not all periodic motion follows this specific pattern, making simple harmonic motion just one type of periodic motion.
Oscillation refers to the back and forth motion of an object around an equilibrium position. Periodic motion is a type of oscillation, as the object repeats its motion at regular intervals. However, not all oscillatory motion is necessarily periodic, as it may not have a specific pattern or frequency.
The period of a periodic motion is affected by several factors, including the mass and stiffness of the object, as well as the strength of the restoring force. In addition, the amplitude and frequency of the motion also play a role in determining the period.
To resolve a periodic motion into oscillatory components, we can use Fourier analysis. This involves breaking down the motion into a series of simple harmonic motions with different frequencies and amplitudes. This allows us to better understand the different components that make up the overall periodic motion.