Important Topic of Physics: Periodic Motion

# Important Topic of Physics: Periodic Motion

## Introduction:

Vibration is defined as a reciprocating motion repeated at regular intervals. During oscillation, the frequency of the oscillation is relatively small. Oscillation is defined as the movement of an object with respect to its average position, and this movement can be linear, circular, periodic, or aperiodic. When the vibration frequency is higher and an external force also acts on the body. In general, we describe the movement of the body as it moves. When an object moves in a way that repeats a path regularly at regular intervals, the motion is said to be periodic. We can classify different body movements according to the way they move. For example, a car traveling on a straight road is said to travel in a straight line. Likewise, the movement of the Earth around the Sun is circular. The movements which are repeated at regular intervals are called periodic motion. After a certain amount of time, the body repeats movements around a certain point along a certain path, called periodic exercise.

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## Overview:

A fixed time interval in which a movement repeats is called a movement period. In order for an object or an object’s motion to be periodic, it must have a certain period and the smallest time interval during which the periodic movement of an object repeats is called the period T.

The motion of a tuning fork or pendulum. If you analyze the movement, you can see that the pendulum passes the intermediate position only after a certain amount of time has elapsed. You can also classify the above movements as vibrations. Oscillating motion is a movement in which an object reciprocates around a fixed position. So, the oscillatory motion can be periodic, but not necessarily. Movements that do not repeat at regular intervals are non-periodic.

 Parameters Periodic Motion Non-Periodic Motion Motion Repeated motion Non-repetitive motion Time The happening of periodic motion is totally related to the time interval. The non-periodic motion didn’t have such a relevance. Time period It has a time period. It has a time of movement. Type of motion Vibratory or oscillatory motion. Displacement of an object Example The movement of a girl who is sitting in the swing. The movement of a sewing machine needle operating at a constant speed. If a load attached to the spring is pulled once a part from its mean position and left to itself starts vibrating. The movement of the tuning fork. An apple falling down from the tree. The movement of the bouncing ball under the action of gravity and friction. The clouds coming together in the sky and their motion. The movement of a vehicle at changing speed. Writing on the paper.

### Periodic Motion Formula:

Time Period (T): It is defined as the total time taken by the motion to repeat itself and generally, the unit of a time period is seconds.

Frequency (f): It is defined as the number of times the motion is repeated in one second and the unit of frequency is Hz (Hertz).

Frequency is related to Time period as:

f=1/T

### Simple Harmonic Motion:

We have also heard of what is known as simple harmonic motion. In reality, it is a periodic motion with some relationship between the restoring force and the displacement in the intermediate position. SHM is a special case of vibration, in which motion occurs in a straight line between two poles. The restoring force appears to be directed towards an intermediate or equilibrium position in simple harmonic motion. The intermediate position in simple harmonic motion is a stable equilibrium.

For decades, the simple harmonic motion has been used as the basis and mathematical model for defining and studying several different periodic motions. The time period of a simple harmonic motion follows the motion of a sine wave and has its own resonant frequency. This resonant frequency is a completely separate and important concept in engineering and instrumentation.

The simple pendulum is the most common example of a body performing an S.H.M. An ideal simple pendulum consists of a heavy body with a point mass suspended on a weightless, tension, and perfectly flexible string on rigid support on which the pendulum can vibrate freely.

Some other examples of simple harmonic motion are spring oscillators, oscillating pendulums, uniform circular motion, oscillating motion, etc.

##### What causes periodic motion?

According to Newton's first law, the law of inertia, an object will move in a straight line if no force is applied to it. A similar concept can be applied to objects in periodic motion. A simple pendulum starts to move back and forth when it is pulled from a rest position (pulling is a kind of force) and tends to vibrate until we continue to apply a force to the pendulum.

##### What is circular motion?

The movement of an object while rotating along a circular path is called circular motion.

##### What is a simple harmonic motion?

Movements in which the restoring force is directly proportional to the displacement of the body from its average position are called simple harmonic motion (SHM).

##### Why is harmonic motion periodic?

Harmonic motion, like any other periodic motion, is said to be periodic because it repeats at regular intervals and exhibits symmetry in motion. Simple harmonic motion consists essentially of a mass/object moving towards an equilibrium position in its range of motion without loss of energy (in ideal conditions, in practice the motion will decay after some time due to the drag force acting on the body) and it will repeat.

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