Phase Mechanics

Phase mechanics is an important phenomenon related to the SHM and periodic function of waves. In this article, you will read about the phase mechanics, equation of phase mechanics, simple harmonic motion, phase angle and its measurement.

What is Phase in Mechanics?

The time required by a point to complete a full cycle after passing through the reference position, or zero position, is known as the phase in mechanics. To understand this, let’s take the example of a clock. In a clock, the reference position for the needles is always at the number 12, and the period of one hour comes under the minute needle.

So, the minute needle has a phase of one-fourth period at one-fourth of the hour time, which passes through a phase angle of π/2 radians or 90°. Hence it is clear that the motion of the minute needle in this example is a uniform circular motion, but the concept of phase is also applicable to simple harmonic motion such as the waves and vibrating bodies.

Equation of Phase Mechanics

Since angle Φ denotes the phase difference of a sinusoidal waveform, and when the waveform changes from a particular reference point along the horizontal zero axes, the phase difference or phase shift is measured in terms of radians or degrees. In other words, we can conclude that the parallel difference between two or more waveforms along a mutual axis is known as phase difference.

So, the general expression of the phase mechanics equation will be written as:

A = A_max sin (ωt ±Φ)

Where,

A denotes the amplitude of the given sinusoidal wave

A_max denotes the maximum amplitude of the given sinusoidal wave

ω denotes the angular frequency

Φ denotes the phase angle measured in either radians or degrees

What is Phase Angle?

The phase angle is a basic characteristic of a periodic wave which refers to its angular component. It is measured in degrees or radians, and it is identical to phase in many situations.

A periodic wave is represented as: Aθ

Where,

• A = magnitude
• Θ = phase angle

How to Measure Phase Angle?

The phase angle of a periodic wave can be measured using the following steps:

By angularly measuring the number of units between the point on the wave and the reference point, the phase angle can be measured. The reference point can exist on the same wave or another wave.

The point of reference is selected from the real axis of an Argand diagram to the rotating vector.

Finally, the phase angle of that point can be calculated by finding the value of the point on the abscissa corresponding to the point on the wave.

Watch the video and learn more about the types of waves

Concept of Simple Harmonic Motion

An oscillatory motion in which the acceleration of the particle at any position and its displacement from the mean position is proportional to each other is known as simple harmonic motion. Basically, it is a special case of oscillatory motion.

All oscillatory motions are not SHM, but all simple harmonic motions are periodic as well as oscillatory.

Phase in Simple Harmonic Motion

At any instant of time, the phase of a vibrating particle is the state of an oscillating or vibrating particle concerning its direction and displacement of vibration at that particular instant of time.

The expression for the position of a particle as a function of time can be written as:

x = A sin (ωt + Φ)

Where (ωt + Φ) shows the phase of the particle,

And initial phase is the phase angle at time t = 0

There are basically two types of Simple Harmonic Motion:

Linear Simple Harmonic Motion: When a particle moves back and forth about a fixed equilibrium position point along with a straight line, then this type of motion is named as linear simple harmonic motion.

Angular Simple Harmonic Motion: With respect to a fixed axis, when a system oscillates angularly, then its motion is named as angular simple harmonic motion.

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