What is Simple Harmonic Motion?


A particle is said to execute simple harmonic motion if it moves to and fro about a mean position under the action of a restoring force which is directly proportional to its displacement from the mean position.

If the displacement of the oscillating body from the mean position is small, then
Restoring force ∝ Displacement
F  ∝  x     or     F = -kx
The above equation defines SHM. Where k is a positive constant called force constant or spring factor and is defined as the restoring force produced per unit displacement. The SI unit of k is Nm-1. the negative force represents that restoring force F always acts in the opposite direction of the displacement x.
According to Newton’s second law of motion,
simple harmonic motion - Testbook
So, Simple Harmonic Motion can also be defined as,
A particle is said to possess S.H.M if it moves to and fro about a mean position under an acceleration which is directly proportional to its displacement from the mean position. 
Some examples of Simple Harmonic Motion are:
  1. Oscillation of a loaded spring
  2. Vibrations of a tuning fork
  3. Vibrations of the balance wheel of a watch
  4. A freely suspended magnet in a uniform magnetic field oscillates in a simple harmonic motion.

Important Features of Simple Harmonic Motion

  1. The motion of the particle is periodic
  2. It is the oscillatory motion of the simplest kind in which the particle oscillates back and forth above its mean position with constant amplitude and fixed frequency.
  3. Restoring force acting on the particle is proportional to its displacement from the mean position.
  4. The force acting on the particle always opposes the increase in its displacement
  5. A simple harmonic motion can always be expressed in terms of a single harmonic function of sine or cosine.
Simple Harmonic Motion - Testbook

Important Terms Related to Simple Harmonic Motion

  1. Harmonic Oscillator: a particle executing simple harmonic motion is called a harmonic oscillator.
  2. Displacement: the distance of the oscillating particle from its mean position at any instant is called its displacement. It is denoted by x.
  3. Amplitude: the maximum displacement of the oscillating particle on either side of its mean is called its amplitude.
  4. Oscillation: one complete back and forth motion of a particle starting and ending at the same point is called a cycle or oscillation
  5. Time period: the time taken by a particle to complete one oscillation is called a time period.
  6. Frequency: it is defined as the number of oscillations completed per unit time by a particle.
  7. Angular Frequency: it is the quantity obtained by multiplying frequency by a factor of 2ℼ
  8. Phase: the phase of a vibrating particle at any instant gives the state of the particle as regards its position and the direction of motion at that instant. Suppose a simple harmonic equation is represented by:
x = Acos(ɷt + 𝚹)
Then phase of the particle 𝚹0 = ɷt + 𝚹

Summarized Notes On Simple Harmonic Motion

  1. A particle is said to execute simple harmonic motion if it moves to and fro about a mean position under the action of a restoring force which is directly proportional to its displacement from the mean position.
  2. For a simple harmonic motion, acceleration is directly proportional to the displacement
  3. The equation of SHM can be given by: x = Acos(ɷt + 𝚹)

Hope you understood the concept covered in this article Simple Harmonic Motion.