Simple harmonic motion

Any motion that repeats itself after a certain period is known as a periodic motion, and since such a motion can be represented in terms of sines and cosines it is called a harmonic motion.
Simple harmonic motion (s.h.m. for short) is the name given to a particular type of harmonic vibration. The following are examples of simple harmonic motion:



a test-tube bobbing up and down in water (Figure 1)
a simple pendulum
a compound pendulum
a vibrating spring
atoms vibrating in a crystal lattice
a vibrating cantilever
a trolley fixed between two springs
a marble on a concave surface
a torsional pendulum
liquid oscillating in a U-tube
a small magnet suspended over a horseshoe magnet
an inertia balance

Simple harmonic motion is defined as follows:



The equations for simple harmonic motion can be written as follows:



where k is a constant and x is the displacement of the body from the fixed point at any time t.



The maximum displacement of the body on either side of its central position is called the amplitude (r).
The period of the motion (T) is the time it takes for the body to make one complete oscillation.



where w is a constant (not to be confused with angular velocity). The value of w depends on the particular system of oscillation.