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,
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:
- Oscillation of a loaded spring
- Vibrations of a tuning fork
- Vibrations of the balance wheel of a watch
- A freely suspended magnet in a uniform magnetic field oscillates in a simple harmonic motion.
Important Features of Simple Harmonic Motion
- The motion of the particle is periodic
- 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.
- Restoring force acting on the particle is proportional to its displacement from the mean position.
- The force acting on the particle always opposes the increase in its displacement
- A simple harmonic motion can always be expressed in terms of a single harmonic function of sine or cosine.
Important Terms Related to Simple Harmonic Motion
- Harmonic Oscillator: a particle executing simple harmonic motion is called a harmonic oscillator.
- Displacement: the distance of the oscillating particle from its mean position at any instant is called its displacement. It is denoted by x.
- Amplitude: the maximum displacement of the oscillating particle on either side of its mean is called its amplitude.
- Oscillation: one complete back and forth motion of a particle starting and ending at the same point is called a cycle or oscillation
- Time period: the time taken by a particle to complete one oscillation is called a time period.
- Frequency: it is defined as the number of oscillations completed per unit time by a particle.
- Angular Frequency: it is the quantity obtained by multiplying frequency by a factor of 2ℼ
- 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
- 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.
- For a simple harmonic motion, acceleration is directly proportional to the displacement
- The equation of SHM can be given by: x = Acos(ɷt + 𝚹)
Hope you understood the concept covered in this article Simple Harmonic Motion.
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