Simple harmonic vibration is the most basic and simple mechanical vibration. When an object is in simple harmonic vibration,

The force on an object is proportional to the displacement and always points to the equilibrium position.

If f represents the restoring force of the object and x represents the displacement of the ball to the equilibrium position, according to Hooke's law,

F and x are in direct proportion, and the relationship between them is: F =-kx.

Where k is the stiffness coefficient of the spring; The negative sign indicates that the direction of restoring force is always opposite to the direction of object displacement.

According to Newton's second law, F=ma, the acceleration of a moving object is always proportional to the resultant force on the object.

In direct proportion to the resultant force, in the same direction.

The frequency (or period) of simple harmonic vibration has nothing to do with amplitude. The vibration frequency of an object is determined by its nature, so it is also called natural frequency.

The motion made by the projection of an object in uniform circular motion on the diameter is simple harmonic motion:

R is the radius of uniform circular motion and the amplitude of simple harmonic motion;

ω is the angular velocity of uniform circular motion, also called the circumferential frequency of simple harmonic motion, ω = √ (k/m);

Φ is the angle at which an object moving in a uniform circular motion deviates from its diameter when t=0 (counterclockwise is the positive direction), which is called the initial phase of simple harmonic motion.

At time t, the displacement of simple harmonic motion x=Rcos(ωt+φ), and the velocity of simple harmonic motion v=-ωRsin(ωt+φ).

The acceleration of simple harmonic vibration is a =-(ω 2) rcos (ω t+φ), and these three equations are called simple harmonic vibration equations.

It is assumed that this motion occurs without energy loss leading to damping.