Simple harmonic motion summary

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Harmonics in simple harmonic motion (SHM) refer to the periodic oscillations characterized by a linear relationship between the restoring force and displacement. The motion can be described by a second order differential equation, indicating that without damping, the system behaves predictably. The total energy of an undamped oscillator remains constant, comprising both kinetic and potential energy. Damping can affect the motion, introducing energy loss over time. Understanding these principles is essential for analyzing periodic motion in various physical systems.
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What is mean by harmonics in SHM?
 
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Here is nice summary - http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html

More generally - periodic motion - http://hyperphysics.phy-astr.gsu.edu/hbase/permot.html#permot

Simple harmonic motion implies a linear relationship between a restoring force, which is a function of displacement from some reference location, and acceleration (as opposed to non-linear). Damping may be invovled.

Without damping the equation of motion is given by a second order differential equation

m\ddot{x}\,+\,kx\,=\,0[/itex],<br /> <br /> and the total energy for an undamped oscillator, which is the sum of its kinetic energy and potential energy, is constant.
 

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