Relation Between Phase and Frequency

In physics, simple harmonic motion is the repetitive movement between an object’s initial and final positions through an equilibrium. The force responsible for the motion is always directed to the equilibrium spot and is equal to the distance from it. The mathematical expression for harmonic motion is F= -kx, where F indicates the force, x is displacement, and k is a constant. This relation is known as Hooke’s Law.

Simple Harmonic Motion

Characteristics of Simple harmonic motion

1. The motion is in a straight line.
2. Force and acceleration are directly proportional to displacement.
3. The motion will be oscillatory.
4. The time of oscillation is independent of amplitude. The oscillation depends upon the force constant and mass of the body.

Examples of Simple harmonic motion

1. The motion of a simple pendulum
2. Vibration In a mass and spring system
3. The oscillations inside a U-tube.
4. The oscillations of a floating object.

Phase and phase difference

The Phase of a vibrating substance defines what stage of vibration the substance is at that point.

It is expressed by an angle at which the given substance has been traced in the central point of the reference circle since it last passed through that point, corresponding to the equilibrium point of that vibrating substance.

The phase difference between two vibrating substances signifies how much they are out of step. If the phase difference between two substances vibrating with the same Frequency stands to be zero, the two substances will pass back and forth about their mean positions; they are said to be in opposite phases. The substances will be in the opposite phases if the phase difference is 180 degrees.

Frequency & Acceleration

The frequency of oscillation is simply defined as the total number of oscillations in one second. In ​T​ seconds, the object completes in one oscillation. The oscillation frequency is measured in terms of cycles per second or Hertz.

The rate at which the velocity changes with time, in terms of speed and direction, is known as acceleration.

Time & Amplitude

The period is the total time taken by the particle to complete one oscillation. T. indicates That time and frequency are inversely proportional to each other.

The maximum displacement of a particle in simple harmonic motion is called amplitude. The energy of the whole system depends on the amplitude A. 

Angular oscillations & angular frequency

When a body is made to rotate freely about a fixed axis, its rotation is called angular oscillation. The position at which the resultant torque is zero is known as the mean or initial position.

Angular Frequency is a physical quantity that measures the speed at which an object rotates or oscillates over time. It is usually indicated by the letter Ω. It is expressed in terms of radians per second, which is the S.I. unit.

Relation between Phase and Frequency

The frequency is inversely proportional to the time interval for 1 degree of phase. The frequency of a signal is given by f, and the time the (in secs) regarding one degree of phase is the = 1 / (360f) = T / 360. Therefore, a one-degree phase shift on a 5 MHz signal shows a time shift of 555 picoseconds.

Time And Frequency Relationship

Frequency, f, is the total number of rotation cycles occurring per second and is measured in cycles per second or hertz (Hz). The period of a wave, T, is the total amount of time it takes a wave to vibrate one complete full cycle. These two expressions are inversely proportional to f = 1/T, while T = 1/f.

Conclusion

Simple harmonic motion is necessary for understanding the theory of oscillations of waves. It is defined by easily recognizable characteristics and numerous applications in Physics, such as in simple pendulums and mass-spring systems. The relations between terms such as Time And Frequency, Phase and Frequency, and Phase and Phase difference help us understand the concepts much better.