What is Periodic Motion?
We generally describe the motion of bodies in the way they move. If an object moves such that it repeats its path regularly after equal intervals of time, it's motion is said to be periodic. Such motion is characterized by the angular frequency, where the body displaces by some angle at some speed called the angular speed given by,
Here, Ω = 2 πf, Ω is the angular speed and f is the frequency. This motion can be represented by a sinusoidal wave as shown below:
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You have seen in schools that each lecture is allotted a fixed interval of time. This fixed interval of time is called the time period however the teacher coming and leaving your class daily is the periodic motion of your teacher.
Periodic Motion Definition
If a body recurs its motion along a definite path, about a certain point after a fixed interval of time is called the periodic motion. The fixed interval of time after which the motion is repeated is called the period of motion. The requirement that the motion of a body or an object must satisfy to be periodic is that it possesses a definitive period where the least interval of time after which the periodic motion of a body repeats itself is called the period T.
Give two Examples of Periodic Motion
The motion of the hands of a clock. The period of motion of an hour’s hand is 12 hrs, of a minute’s hand is 1 hour and of the second’s hand of a clock is 1 minute.
A simple pendulum, when pulled from its rest position to one side and released, makes to and fro motion (oscillatory motion) is said to be periodic.
Non - Periodic Motion
The type of motion in which the object repeats its motion but not in a fixed interval or period of time. Let’s take the example of a taxi service that provides the inter-city services to the public but there are plenty of taxis to drop the passengers. Each taxi isn’t having a fixed interval of time and not even sure of which taxi would come to pick the passengers at a stop. Such a condition where the pattern isn’t fixed, the motion of these taxis is said to be in non-periodic motion.
Non-periodic motion examples
The running of the batsman between the wickets.
The swinging of the branches of the tree.
The periodic motion and non-periodic motion differ from each other in their way of existence in nature, that are as follows:
Difference Between Periodic and Non-Periodic Motion
Do you know?
The period of revolution of the earth around the sun is one year.
The period of rotation of the earth about its polar axis is one day.
The period of rotation of the moon around the earth in 27.3 days.
The oscillatory motion can be expressed in sine or cosine waves or their combinations. It is due to the reason that the oscillatory motion is called harmonic motion.
The time period of a simple pendulum of infinite length is equal to the radius of the earth i.e. 84.6 minutes.
The time period of a pendulum clock in a lift falling freely under gravity is infinite.
Simple Harmonic Motion (SHM)
A common and widely studied type of periodic motion is the Simple Harmonic Motion (SHM). In an ideal system (system with no resistive force to the moving object), the object that moves in the system derives restoring force such that the system can move from the extreme point on one end to the equilibrium position and then to the other extreme end in an oscillatory way for an indefinite amount of time. In ideal conditions, the motion does not experience a damping effect.
For decades, simple harmonic motion has served as the basis and mathematical model to define and study several other periodic motions. The time period in a simple harmonic motion follows the motion of a sinusoidal wave and has a distinct resonant frequency. This resonant frequency is an altogether distinct and important concept for engineering and instrumentation fields.
Some examples of simple harmonic motion are the mass-spring oscillator, the oscillating pendulum, uniform circular motion, oscillatory motion, etc.
FAQs on Periodic Motion
1. What is periodic motion?
Periodic motion is a type of motion where an object or a body repeats its path over a regular, fixed interval of time. This fixed time interval is known as the time period (T). For a motion to be classified as periodic, the key condition is its repetitive nature at constant time intervals.
2. What are some common examples of periodic motion in daily life?
Many phenomena around us exhibit periodic motion. Some common examples include:
- The revolution of the Earth around the Sun (time period: 1 year).
- The rotation of the Earth on its axis (time period: 24 hours).
- The motion of the hands of a clock.
- A simple pendulum swinging back and forth.
- The vibrations of a guitar string after being plucked.
3. What is the difference between periodic motion and oscillatory motion?
While related, they are not the same. Periodic motion is any motion that repeats itself after a fixed time interval. Oscillatory motion is a specific type of periodic motion where the object moves back and forth about a central, or equilibrium, position. A classic example of oscillatory motion is a swinging pendulum.
4. Are all periodic motions oscillatory? Explain why or why not.
No, not all periodic motions are oscillatory. An oscillatory motion must be a to-and-fro movement about a mean position. However, a periodic motion only needs to repeat itself in a fixed time. For example, the uniform circular motion of a planet around the sun is periodic because it repeats its path in a fixed time, but it is not oscillatory because it does not move back and forth about a central point.
5. How are time period (T), frequency (f), and angular frequency (ω) related in periodic motion?
These three quantities are fundamental to describing periodic motion and are interrelated.
- The Time Period (T) is the time taken to complete one full cycle of motion.
- The Frequency (f) is the number of cycles completed per unit of time. It is the reciprocal of the time period, so f = 1/T.
- The Angular Frequency (ω) represents the rate of change of phase angle, measured in radians per second. It is related to frequency by the formula ω = 2πf, or ω = 2π/T.
6. Why is Simple Harmonic Motion (SHM) considered a special type of periodic motion?
Simple Harmonic Motion (SHM) is a special and the simplest form of oscillatory motion. What makes it unique is the nature of the restoring force. In SHM, the restoring force acting on the object is directly proportional to its displacement from the mean position and is always directed towards that mean position. This relationship is expressed as F = -kx, where k is the force constant. While all SHM is periodic, not all periodic motion follows this specific force condition.
7. What happens to the total energy of a particle executing Simple Harmonic Motion?
In an ideal system with no friction or air resistance (undamped SHM), the total mechanical energy (sum of kinetic and potential energy) of a particle executing SHM remains constant. The energy continuously transforms between kinetic and potential forms. At the mean position, kinetic energy is maximum and potential energy is zero. At the extreme positions, potential energy is maximum while kinetic energy is zero. However, the total energy at any point in the path remains conserved.
