Under the action of restoring force proportional to displacement, an object reciprocates according to sine law near its equilibrium position. Simple harmonic vibration is the most basic and simple mechanical vibration. When an object is in simple harmonic vibration, the force on the object is proportional to the displacement and always points to the equilibrium position. It is a periodic movement determined by the nature of its own system. Simple harmonic vibration is actually sinusoidal vibration. Simple harmonic vibration is the simplest and most basic vibration, and any complex vibration can be regarded as the synthesis of several simple harmonic vibrations.
The basic laws of vibration and fluctuation are the basis of acoustics, seismology, electrotechnics, electronics and optics.
We can say that the displacement is a sine or cosine function of time t and the motion is simple harmonic motion. The mathematical model of simple harmonic vibration is linear constant coefficient ordinary differential equation, and such vibration system is called linear system. Linear system is the simplest and most common mathematical model of vibration system.