Waves-Periodic Motion

An oscillation is a motion that foreseeably plays out over and over. In contrast, a wave is an oscillation that is going somewhere. For example, a pendulum is oscillatory. The pendulum’s bob rises while it swings to the right and then it falls and then it rises again when it swings back to the left. Another example is when we drive our car over a bump, the car vertically oscillates. 

Wave is a spreading dynamic disturbance of one or more quantities. Waves are vibrational disturbances that travel through a medium. The most common example is the water waves. A wave will make the objects on it go up and down. When a wave moves towards a direction, it makes the object go up and down. 

What is periodic motion?

A simple Periodic motion definition is a motion that is repeated in equal intervals. A motion that is regular and repeating is called periodic motion. The objects that vibrate do so in a regular fashion, meaning it’s periodic. Consider a vibrating object moving over the same path over time. 

The motion keeps repeating; the time it takes to complete one motion, i.e. one back and forth, is similar. The motion of a pendulum, spring, rocking chair, bouncing ball vibration of guitar strings, even the earth’s rotation over its axis, revolving around the mighty sun, follows a periodic motion. In these cases, the time interval, repetition or the cycle of motion is called a period and the number of periods per unit time is known as frequency. 

How can you calculate periodic motion?

The periodic motion definition is a motion that repeats itself repeatedly. In contrast, the time required for one repetition is called period(T) and one complete cycle of this motion is known as a cycle. The (f) frequency can be defined as the count of cycles per time unit.

f = 1/T

For example, consider a newborn baby’s heart that is beating at the rate of 150 times a minute. The period, i.e. the interval between beats, is half a second.

Periodic motion is expressed best in angular frequency terms represented by the omega letter. Angular frequency is the angular displacement per unit time, the rate of change of the phase of the sinusoidal waveform.

Simple oscillator (harmonic) time period

The simple oscillator (harmonic) is termed the most common type of periodic motion. It is defined as the motion in which the acceleration is always proportional to the length/distance from the stage of its equilibrium. 

T = 2π​ /ω

Where ω is the angular frequency of the oscillator.

Pendulums as well as springs: periodic motion 

A mass on the spring is subjected to a force ​F​ = −​kx (k is termed as the characteristic of spring). Newton’s second law proves this force equal to the body’s mass(m) times the acceleration, ma = -kx

T = 2π √ k/m​

Examples of periodic motion

The name itself suggests that examples of periodic motion are all around us, from a rocking chair, vibrating fork, a ball bouncing, a swing in motion, the earth revolving around the sun, and water waves.

• Swinging pendulum

A swinging pendulum that is swinging continuously with a fixed time period is an example of periodic motion. A constant to and fro motion that the pendulum follows makes it a good example.

• Rocking chair

The rocking chair again rocks in a to and fro motion with a fixed time period. This is one of the most common examples of periodic motion.

• Revolution of Earth

The Revolution of the earth around the sun, which takes 365 days and 6 hours to complete, is a periodic motion.

• Hands of a clock

The hands of a clock that makes 360-degree rotation is an example of periodic motion.

• Heartbeat

Heartbeat, which beats at around 70 to 100 beats per minute, is another example of periodic motion.

• Revolution of an electron around a nucleus

An electron that revolves around a positively charged nucleus is an example of periodic motion.

Conclusion

An oscillation is a motion that repeatedly occurs, whereas waves are oscillations that move in a different direction. The process in which physical quantity changes periodically is called oscillation. Vibrations are also used to describe mechanical oscillation. Oscillations occur in dynamic systems other than just mechanical systems, for example, heartbeat guitar strings vibrations.

In contrast, the wave is a spreading dynamic disturbance of one or more quantities. Waves can be recurring and the quantities repeatedly oscillate about an equilibrium value at a frequency. The most commonly studied waves are mechanical and electromagnetic waves.