Restoring force, in a physics context, is a force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back toward equilibrium.
Period
A time period (denoted by 'T' ) is the time needed for one complete cycle of vibration to pass in a given point.
Frequency
Frequency, in physics, the number of waves that pass a fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.
Amplitude
The amplitude of a periodic variable is a measure of its change over a single period.
Angular Frequency
In physics, angular frequency ω is a scalar measure of rotation rate. It refers to the angular displacement per unit time or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument of the sine function.
Energy Transfers
Simple harmonic motion is any periodic, repetitive motion where a restoring force is applied that is proportional to the displacement, in the opposite direction of that displacement. ... And kinetic energy is the energy any moving object has, which is proportional to the square of the velocity of that object.
What Affects Period?
The mass and the force constant are the only factors that affect the period and frequency of simple harmonic motion.
Inertial vs Gravitational Mass
Inertial mass measures an object's resistance to being accelerated by a force (represented by the relationship F = ma). Active gravitational mass measures the gravitational force exerted by an object.
Proving Simple Harmonic Motion
In mechanics and physics, simple harmonic motion is a type of periodic motion or oscillation motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement .
Therefore, in order to prove that something is SHM, you must prove that the Restoring Force is directly proportional to the displacement.