In physics, simple harmonic motion (SHM) is the motion of a simple harmonic oscillator, a motion that is neither driven nor damped. A body in simple harmonic motion experiences a single force which is given by Hooke's law; that is, the force is directly proportional to the displacement x and points in the opposite direction.
The motion is periodic: the body oscillates about an equilibrium position in a sinusoidal pattern. Each oscillation is identical, and thus the period, frequency, and amplitude of the motion are constant. If the equilibrium position is taken to be zero, the displacement x of the body at any time t is given by
where A is the amplitude, f is the frequency, and φ is the phase.
The frequency of the motion is determined by the intrinsic properties of the system (often the mass of the body and a force constant), while the amplitude and phase are determined by the initial conditions (displacement and velocity) of the system. The kinetic and potential energies of the system are also determined by these properties and conditions.
Simple harmonic motion.Simple harmonic motion can serve as a mathematical model of a variety of motions, such as the oscillation of a spring. Other phenomena can be approximated by simple harmonic motion, including the motion of a pendulum and molecular vibration.
Simple harmonic motion provides the basis of the characterization of more complicated motions through the techniques of Fourier analysis.
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