Simple harmonic motion summary

[deshmukhnm]

What is mean by harmonics in SHM?

 

[Astronuc]

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

[tex] m\ddot{x}\,+\,kx\,=\,0[/itex],

and the total energy for an undamped oscillator, which is the sum of its kinetic energy and potential energy, is constant.

 

[charng]

Simple harmonic motion (SHM) is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point due to a restoring force. This type of motion can be observed in various physical systems, such as a mass attached to a spring or a pendulum.

Harmonics in SHM refer to the different frequencies at which the object oscillates. The fundamental frequency is the lowest frequency at which the object can oscillate, while the higher frequencies are known as harmonics. These harmonics are integer multiples of the fundamental frequency, meaning that they occur at regular intervals.

In SHM, harmonics play an important role in determining the characteristics of the motion, such as the amplitude and period. The presence of harmonics also allows for the formation of complex wave patterns, which can be observed in systems like musical instruments.

Overall, harmonics in SHM help us understand the behavior of oscillating systems and can be used to analyze and predict their motion.