What is mean by harmonics in SHM?
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
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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