Simple harmonic motion (SHM) is a type of periodic motion exhibited by certain systems in which an object oscillates back and forth around a stable equilibrium position. It follows a specific pattern where the displacement of the object from the equilibrium position is directly proportional to the restoring force acting on it and is opposite in direction to the displacement.
For an object to undergo simple harmonic motion, certain conditions need to be met:
Restoring Force: There must be a restoring force acting on the object, which is proportional to the displacement and directed towards the equilibrium position. The restoring force aims to bring the object back to its equilibrium position when it is displaced.
Linearity: The system's motion must be linear, meaning that the force acting on the object is directly proportional to the displacement. This condition allows for a simple relationship between the force and displacement.
Small Amplitude: Simple harmonic motion typically assumes small displacements from the equilibrium position. This condition ensures that the motion is linear, as a larger displacement may introduce non-linear effects and alter the behavior of the system.
No Damping: In ideal simple harmonic motion, there is no external damping force acting on the object. Damping refers to the dissipation of energy, which leads to a gradual decrease in the amplitude of oscillation over time. By assuming no damping, the system's energy remains constant, resulting in perpetual oscillations.
No External Forces: In ideal SHM, there are no other external forces acting on the object apart from the restoring force. This condition ensures that the motion is solely governed by the interplay between the restoring force and the object's inertia.
Examples of systems that exhibit simple harmonic motion include a mass-spring system (e.g., a mass attached to a spring), a pendulum, and vibrations of a guitar string.
Simple harmonic motion is characterized by a sinusoidal waveform, with quantities such as displacement, velocity, and acceleration following harmonic functions. These quantities oscillate periodically with a constant frequency, amplitude, and phase relationship.
The mathematical description of simple harmonic motion involves concepts such as angular frequency, period, frequency, amplitude, and phase, which provide a quantitative understanding of the motion and its characteristics.