Terminology Related to Simple Harmonic Motion

There are various terminologies related to SHM (Simple Harmonic Motion) some of which are explained as follows:

Mean Position

In Simple Harmonic Motion, the position of the object where there is no restoring force acting on it is the mean position. In other words, the point about which the object moves between its extreme position is called the mean position of the object. The mean position is sometimes referred to as Equilibrium Position as well.

Amplitude

The amplitude of a particle in SHM is its maximum displacement from its equilibrium or mean position, and as displacement is a vector quantity, its direction is always away from the mean or equilibrium position. The SI unit of amplitude is the meter and all the other units of length can also be used for this.

Frequency

The frequency of SHM is the number of oscillations performed by a particle per unit of time. SI unit of frequency is Hertz or r.p.s. (rotations per second), and is given by:

• Frequency

f = 1/ T

• Angular Frequency

ω = 2πf = 2π/T 

Time Period

For a particle performing SHM, the time period is the amount of time it takes to complete one complete oscillation. As a result, the time period or simply period of SHM is the shortest time before the motion repeats itself.

T = 2π/ω 

 where ω is the Angular frequency and T is the Time period.

Phase

The phase of SHM represents the magnitude and direction of particle displacement at any instant of the motion which is its state of oscillation.

The expression for a particle’s position as a function of time and angular frequency is as follows:

x = A sin (ωt + ϕ)

where (ωt + ϕ) is the phase of particle.

Phase Difference

For two particles performing SHM, the phase difference is defined as the difference between the total phase angles of those particles. Phase Difference is denoted by Δϕ. Mathematically the phase difference is defined as the difference between the total phase angles of two particles moving in simple harmonic motion with respect to the mean position. 

For example, for two particles performing SHM with the same angular frequency with displacement functions, x₁ = A sin (ωt + ϕ₁) and x₂ = A sin (ωt + ϕ₂). The phase difference is given by 

Δϕ =  ϕ₁ – ϕ₂

When two vibrating particles with the same angular frequency, are in the same phases if the phase difference between them is an even multiple of π i.e.,

Δϕ = nπ

Where, n = 0, 1, 2, 3, 4, . . . 

Two vibrating particles with the same angular frequency, are said to be in opposite phases if the phase difference between them is an odd multiple of π i.e.,

Δϕ = (2n + 1)π 

Where, n = 0, 1, 2, 3, 4, . . . 

Simple Harmonic Motion is a fundament concept in the study of motion, especially oscillatory motion; which helps us understand many physical phenomena around like how strings produce pleasing sounds in a musical instrument such as the sitar, guitar, violin, etc., and also, how vibrations in the membrane in drums and diaphragms in telephone and speaker system creates the precise sound. Understanding Simple Harmonic Motion is key to understanding these phenomena. 

In this article, we will grasp the concept of Simple Harmonic Motion (SHM), its examples in real life, the equation, and how it is different from periodic motion.