However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law. If the system is left at rest at the equilibrium position then there is no net force acting on the mass. The other end of the spring is connected to a rigid support such as a wall.
In the diagram, a simple harmonic oscillator, consisting of a weight attached to one end of a spring, is shown. (Here the velocity and position axes have been reversed from the standard convention to align the two diagrams) Simple harmonic motion shown both in real space and phase space. The motion of a particle moving along a straight line with an acceleration whose direction is always towards a fixed point on the line and whose magnitude is proportional to the distance from the fixed point is called simple harmonic motion. Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of Fourier analysis. Simple harmonic motion can also be used to model molecular vibration. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small see small-angle approximation). The motion is sinusoidal in time and demonstrates a single resonant frequency.
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. It results in an oscillation that is described by a sinusoid which continues indefinitely (if uninhibited by friction or any other dissipation of energy). In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion an object experiences due to a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position.
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