A harmonic oscillator is a system that exhibits periodic motion, meaning it repeats the same motion over and over again. It can be a physical system, such as a mass on a spring, or a mathematical model, such as a simple pendulum.
The equation for a harmonic oscillator is F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement from equilibrium. This equation is known as Hooke's Law.
The mass affects the motion of a harmonic oscillator by determining the period and frequency of the oscillation. A larger mass will have a longer period and lower frequency, while a smaller mass will have a shorter period and higher frequency.
The spring constant and the period of a harmonic oscillator have an inverse relationship. As the spring constant increases, the period decreases. This means that a stiffer spring will cause the system to oscillate faster, resulting in a shorter period.
In a harmonic oscillator, energy is constantly being exchanged between kinetic energy and potential energy. As the system oscillates, the energy is constantly shifting back and forth between the two forms. The total energy of the system remains constant, but the amount of kinetic and potential energy changes as the oscillator moves through its motion.