Periodic Motion - Definition, Examples, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 05:00 PM IST

Periodic motion is a fundamental concept that undergoes regular repetition over a cycle. It is involved in many objects of the natural world and human-made devices from the swinging of a pendulum to the blades of a fan. Knowledge of periodic motion helps to consider such issues as sound waves and light waves or the motion of celestial objects.

This Story also Contains

What is Periodic Motion?
Characteristics of Periodic Motion
Types Of Periodic Motion
Examples of Periodic Motion

Periodic Motion - Definition, Examples, FAQs

What is Periodic Motion?

Periodic Motion occurs when a system or an object repeats its motion after a fixed interval of time, called as Period (denoted by T). Periodic motion is observed in multiple forms and scales, from microscopic particles to macroscopic mechanical systems.

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Periodic motion in Physics is governed by Newton's laws of motion and can often be described by differential equations. For instance, the equation of motion for a simple harmonic oscillator is:

$$
m \frac{d^2 x}{d t^2}+k x=0
$$

where $m$ is the mass, and $k$ is the spring constant.

Characteristics of Periodic Motion

Below points shows the measurable characteristics of Periodic Motion which helps in its analysis:

Period (T): The time taken for one complete cycle of motion.
Frequency ( f ): The number of cycles per unit time, given by $f=\frac{1}{T}$.
Amplitude (A): The maximum displacement from the equilibrium position.
Phase: Indicates the position and direction of the oscillating object at a specific instant.

Types Of Periodic Motion

Periodic motion is majorly divided into five basic types. Let's discuss each type:

Simple Harmonic Motion (SHM)
Oscillatory Motion
Circular Motion
Rotational Motion
Wave Motion

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Simple Harmonic Motion (SHM): Motion in which restoring force is directly proportional to the displacement and acts in the opposite direction, then it is called as simple harmonic motion.

Simple harmonic motion can be mathematically represented as:

$$
x(t)=A \cos (\omega t+\phi)
$$

where $\omega=2 \pi f$ is the angular frequency.

Oscillatory Motion: Motion that moves back and forth about an equilibrium position is called as Oscillatory Motion.

Example- Seasaw

Circular Motion: When an object moves in a circular path with a constant angular velocity, its projection on any axis shows periodic motion.

Example- Rotation of Earth

Rotational Motion: Motion that involves rotation of an earth's object around a fixed axis is called as rotational motion.

Example- Blades of a fan

Wave Motion: A periodic disturbance that transfers energy through a medium or space.

Example- Sound waves, electromagnetic waves.

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Examples of Periodic Motion

The revolution of the hands of a wall clock. The periodic time of an hour’s hand of a clock is 12 hrs, of a minute’s hand of a clock is 1 hour, and of the second’s hand of a clock is 1 minute.
A pendulum hung from the wall when pulled from its mean position to one side and loose free makes the pendulum make to and fro motion (oscillatory motion) is said to be periodic.
Oscillating balance wheel
rotating chair
Earth's rotation
Earth's rotation around its axis
Moon's rotation around Earth
Diapason
The blade of the propeller
Hand of the clock
Heart rate

Difference between Periodic and Non-Periodic Motion

Parameters	Periodic Motion	Non-Periodic Motion
Motion	Repeated motion	Non-repetitive motion
Time	The rate of periodic motion is totally dependent on the time interval.	The non-periodic motion doesn’t have such relevance.
Time period	It has a time period	It has a time of motion.
Type of motion	Vibratory or oscillatory motion.	Displacement of an object
Example	Movement of a girl sitting on a swing. The needle movement of the sewing machine runs at a constant speed. When the load attached to the spring is pulled once from its middle position and to the left, the spring begins to oscillate. Mercury in a U-tube Tubular movement. Movement of the mill in the motor during manual operation. The rotation of the moon around the sun.	Motion of a ball under the action of gravity and friction when throne from some distance Clouds gather in the sky and their movements. Vehicle movement at variable speed. Write on paper. A soccer player is running on the grass. A ball rolls on the ground. Perform any activity. Walking on the street. Play games.

Do you know?

• The earth's rotation around the sun is one year.

• The earth's rotation around its polar axis is one day.

• The period of revolution of the moon around the earth is 27.3 days.

• Oscillating motion can be expressed as sine or cosine waves or a combination thereof. It is due to the oscillating motion known as harmonic motion.

• The period of a simple pendulum has infinite length equal to the radius of the earth, i.e. 84.6 minutes.

• The length of time the pendulum clock in the elevator is in free fall under the influence of gravity is infinite.

Frequently Asked Questions (FAQs)

1. What causes periodic motion?

According to Newton's first law, the law of inertia, if no force is applied to an object, the object moves in a straight line. A similar concept applies to objects that move periodically. A simple pendulum, when pulled out of its resting position (tension is a force), starts to move back and forth and tends to swing until we continue to apply force to the pendulum.

2. Why is simple harmonic motion periodic?

A harmonic motion can be represented by a sinusoidal wave motion. When the spring extends from the middle position, it swings back and forth around the middle position under the action of a restoring force that always points to the middle position. The size of the spring is proportional to the displacement of the object from the middle position at any position. This moment in time. There is no friction, and the movement remains periodic. In this case, the harmonic motion is periodic.

3. Can other actions be periodic?

All swing motions are called periodic motions, because each swing is completed in a fixed time interval. All oscillating motions are not periodic, just like the rotation of the earth is periodic, but not oscillating.

4. What are periodic and non-periodic changes?

The changes that occur regularly are called cyclical changes, such as the occurrence of day and night, and changes in the time of your school. Changes that do not occur periodically are called non-periodic changes, such as B. freezing into water.

5. Soldiers walking on the drawbridge are advised to leave the stairs. Why?

It is recommended that soldiers marching on the suspension bridge leave the steps, because in this case, the frequency of the marching steps corresponds to the natural frequency of the suspension bridge, and resonance occurs, which can greatly increase the vibration.

6. The vibrator of the harmonic oscillating single pendulum is made of ice. How will the rotational cycle change as the ice begins to melt?

The period of oscillation of a simple pendulum will remain constant until the position of the center of gravity of the pendulum remaining after the ice melts remains at the fixed position of the suspension. If the center of gravity of the iceberg is upward after melting, the effective length of the pendulum decreases and, therefore, the period of oscillation decreases. Likewise, if the center of gravity shifts downward, the time interval increases.

7. How does periodic motion differ from random motion?

Periodic motion is predictable and repeats in a regular pattern, while random motion is unpredictable and does not follow a set pattern. In periodic motion, you can determine the object's future position based on its current state and the time elapsed, which is not possible with random motion.

8. Can periodic motion occur in more than one dimension?

Yes, periodic motion can occur in multiple dimensions. While simple examples like a pendulum may move in one plane, more complex systems can exhibit periodic motion in two or three dimensions. An example is the motion of a planet orbiting the sun, which is periodic in three dimensions.

9. How does simple harmonic motion differ from general periodic motion?

While all simple harmonic motion is periodic, not all periodic motion is simple harmonic. SHM has a specific mathematical form where acceleration is proportional to displacement, resulting in sinusoidal motion. General periodic motion can have any repeating pattern, not necessarily sinusoidal.

10. Can the amplitude of periodic motion change over time?

Yes, the amplitude of periodic motion can change over time, especially in real-world situations. This change is often due to energy loss through friction or air resistance, causing the motion to gradually decrease in amplitude. This phenomenon is called damping.

11. How does damping affect periodic motion?

Damping reduces the amplitude of oscillations over time due to energy loss, typically through friction or resistance. In underdamped systems, the oscillations gradually decrease in amplitude. In critically damped systems, the motion returns to equilibrium without oscillating, while overdamped systems return to equilibrium slowly without oscillating.

12. What is periodic motion?

Periodic motion is a type of movement that repeats itself at regular intervals. An object in periodic motion follows the same path and returns to its starting position after a fixed amount of time, called the period. Examples include a swinging pendulum or a vibrating guitar string.

13. What is the period of a periodic motion?

The period of a periodic motion is the time it takes for one complete cycle of the motion to occur. It is the time required for the object to return to its initial position and state of motion. The period is typically measured in seconds and is denoted by the symbol T.

14. How is frequency related to period in periodic motion?

Frequency and period are inversely related in periodic motion. Frequency (f) is the number of cycles completed per unit time, while period (T) is the time taken for one cycle. Their relationship is expressed as f = 1/T. As frequency increases, the period decreases, and vice versa.

15. What is amplitude in periodic motion?

Amplitude is the maximum displacement of an object from its equilibrium position during periodic motion. It represents the extent of the motion and determines the energy of the system. In a pendulum, for example, the amplitude is the maximum angle it swings away from the vertical.

16. What is simple harmonic motion (SHM)?

Simple harmonic motion is a special type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and always acts towards the equilibrium position. Examples include an ideal spring-mass system or a simple pendulum with small oscillations.

17. What is the difference between natural and forced oscillations?

Natural oscillations occur at a system's natural frequency without external driving forces, like a pendulum swinging freely. Forced oscillations happen when an external periodic force is applied to the system, which may cause it to oscillate at a frequency different from its natural frequency.

18. What is resonance in periodic motion?

Resonance occurs when the frequency of an applied force matches the natural frequency of an oscillating system. At resonance, even a small periodic driving force can produce large-amplitude oscillations. This phenomenon can be both useful (as in musical instruments) and dangerous (as in bridge collapses).

19. What factors affect the period of a simple pendulum?

The period of a simple pendulum depends primarily on two factors: the length of the pendulum and the acceleration due to gravity. Surprisingly, for small oscillations, the period does not depend on the mass of the bob or the amplitude of the swing. This is known as the isochronous property of pendulums.

20. How does the mass of an object affect its periodic motion?

The effect of mass on periodic motion depends on the system. In a simple pendulum, changing the mass doesn't affect the period for small oscillations. However, in a spring-mass system, increasing the mass increases the period of oscillation. The relationship between mass and frequency also depends on the specific system.

21. What is the difference between longitudinal and transverse waves in periodic motion?

In longitudinal waves, the particles of the medium oscillate parallel to the direction of wave propagation (e.g., sound waves). In transverse waves, the particles oscillate perpendicular to the direction of wave propagation (e.g., waves on a string). Both are examples of periodic motion in wave form.

22. How does temperature affect periodic motion in mechanical systems?

Temperature changes can affect periodic motion in mechanical systems by altering material properties. For instance, higher temperatures can cause thermal expansion, changing the dimensions and potentially the natural frequency of oscillating systems. In springs, heat can affect elasticity, influencing the spring constant and thus the period of oscillation.

23. What is the principle of superposition in periodic motion?

The principle of superposition states that when two or more waves or oscillations occur in the same medium, the resultant displacement at any point is the algebraic sum of the individual displacements. This principle allows us to analyze complex periodic motions by breaking them down into simpler component oscillations.

24. How does the concept of reduced mass apply to periodic motion of two-body systems?

Reduced mass is a calculated value that allows a two-body problem to be treated as an equivalent one-body problem, simplifying the analysis of periodic motion in systems like binary stars or molecular vibrations. It takes into account the masses of both objects and their relative motion, enabling more straightforward calculations of periods and energies.

25. What is the significance of normal modes in coupled oscillators?

Normal modes are particular patterns of motion in a system of coupled oscillators where all parts of the system oscillate at the same frequency. Each normal mode has its own characteristic frequency. Complex motions of coupled systems can be described as a superposition of these normal modes, which helps in analyzing and predicting the behavior of complex oscillating systems.

26. How does periodic motion manifest in quantum mechanical systems?

In quantum mechanics, periodic motion is described by wave functions and energy levels rather than classical trajectories. Systems like the quantum harmonic oscillator exhibit discrete energy levels and probability distributions for position and momentum. The correspondence principle shows how quantum behavior approaches classical periodic motion for large quantum numbers.

27. What is the significance of Lissajous figures in studying complex periodic motions?

Lissajous figures are the patterns traced by a system undergoing simultaneous oscillations in perpendicular directions. These figures provide a visual representation of the frequency ratio and phase difference between two periodic motions. They are useful in analyzing complex vibrations, tuning musical instruments, and in electronic test equipment for comparing frequencies.

28. How does the concept of effective spring constant apply to more complex oscillating systems?

The effective spring constant is a useful concept for simplifying the analysis of complex oscillating systems. It allows systems with multiple springs or more complex restoring forces to be treated as equivalent simple spring systems. This concept is applied in various fields, from mechanical engineering to atomic physics, to model and understand periodic motions in complex structures.

29. What is parametric resonance, and how does it differ from forced resonance?

Parametric resonance occurs when a system parameter (like length or spring constant) is varied periodically, as opposed to applying a periodic external force. It can lead to instability and large amplitude oscillations, even when the parameter variation frequency is not equal to the natural frequency. This differs from forced resonance, where the driving frequency matches the natural frequency.

30. What is the relationship between periodic motion and conservation laws?

Periodic motion often exemplifies important conservation laws:

31. How do boundary conditions affect periodic motion in continuous systems?

Boundary conditions significantly influence periodic motion in continuous systems like strings, membranes, or fluid columns:

32. What is the role of restoring force in periodic motion?

The restoring force is crucial in periodic motion as it always acts to bring the object back towards its equilibrium position. This force is responsible for maintaining the oscillations. In a spring system, for example, the restoring force is provided by the spring's elasticity.

33. How do springs exhibit periodic motion?

Springs exhibit periodic motion when stretched or compressed from their equilibrium position. The spring force acts as the restoring force, pulling the spring back towards its equilibrium position. This results in oscillations that, in an ideal system, continue indefinitely with constant amplitude.

34. How does energy change during periodic motion?

In ideal periodic motion, energy constantly transforms between potential and kinetic forms while the total energy remains constant. At the extremes of motion, all energy is potential. At the equilibrium position, all energy is kinetic. This continuous energy conversion maintains the motion.

35. What is phase in periodic motion?

Phase in periodic motion refers to the position and direction of motion of an oscillating object at a particular instant of time. It is often expressed as an angle, with one complete oscillation corresponding to 360 degrees or 2π radians. Two objects in periodic motion can be in phase, out of phase, or have any phase difference in between.

36. How does air resistance affect periodic motion?

Air resistance acts as a damping force in periodic motion, gradually reducing the amplitude of oscillations over time. It converts mechanical energy into heat, causing the motion to eventually stop unless energy is continuously supplied. The effect is more pronounced for objects with larger surface areas or moving at higher speeds.

37. What is the significance of the equilibrium position in periodic motion?

The equilibrium position is the reference point in periodic motion where the net force on the object is zero. It's the position the object would maintain if not disturbed. In oscillatory motion, the object repeatedly passes through this position, having maximum speed but zero displacement at this point.

38. How do coupled oscillators behave in periodic motion?

Coupled oscillators are two or more interconnected oscillating systems that can exchange energy. Their behavior can be complex, exhibiting phenomena like synchronization, where they align their frequencies and phases, or beat phenomena, where the amplitude of oscillation varies periodically due to energy exchange between the oscillators.

39. What is the relationship between periodic motion and waves?

Periodic motion is fundamental to wave propagation. Waves are disturbances that propagate through a medium, carrying energy without transferring matter. The oscillations of particles in the medium create the wave. The frequency and amplitude of these oscillations determine the properties of the wave, such as its wavelength and energy.

40. How does gravity affect periodic motion on different planets?

Gravity plays a crucial role in many types of periodic motion, such as pendulums and orbital motion. The strength of gravity affects the period of oscillation. For example, a pendulum on the Moon would swing more slowly than on Earth due to the Moon's weaker gravity. This principle applies to any periodic motion influenced by gravitational forces.

41. What is anharmonic motion, and how does it differ from simple harmonic motion?

Anharmonic motion is a type of periodic motion that deviates from simple harmonic motion. While SHM follows a perfect sinusoidal pattern, anharmonic motion can have a more complex waveform. The restoring force in anharmonic motion is not directly proportional to displacement, leading to variations in period and frequency with amplitude.

42. How do nonlinear effects influence periodic motion?

Nonlinear effects in periodic motion can lead to complex behaviors not seen in linear systems. These can include amplitude-dependent frequencies, multiple equilibrium positions, and chaotic motion. Nonlinear systems may exhibit phenomena like period doubling or jump phenomena, where small changes in parameters can lead to sudden, large changes in behavior.

43. What is the role of initial conditions in periodic motion?

Initial conditions, such as the starting position and velocity, play a crucial role in determining the subsequent motion in periodic systems. While they don't typically affect the period or frequency of the motion, they determine the amplitude and phase of the oscillations. In some nonlinear systems, initial conditions can even lead to qualitatively different long-term behaviors.

44. How does periodic motion relate to circular motion?

Periodic motion and circular motion are closely related. The projection of uniform circular motion onto a straight line results in simple harmonic motion. This relationship is fundamental in understanding oscillations and waves. It's why the motion of a piston in an engine (approximately SHM) is driven by the circular motion of a crankshaft.

45. What is the significance of Hooke's Law in periodic motion?

Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium, is fundamental to many types of periodic motion. It provides the restoring force necessary for simple harmonic motion in spring systems and serves as a good approximation for many natural oscillators over small displacements.

46. How do standing waves relate to periodic motion?

Standing waves are a special case of periodic motion where waves traveling in opposite directions interfere to produce a wave that appears to stand still. The resulting pattern has nodes (points of no motion) and antinodes (points of maximum motion). Standing waves are important in understanding resonance in strings, air columns, and other oscillating systems.

47. What is the difference between free and forced vibrations?

Free vibrations occur at a system's natural frequency when it's disturbed from equilibrium and left to oscillate on its own. Forced vibrations happen when an external periodic force is continuously applied to the system. While free vibrations will eventually die out due to damping, forced vibrations can be maintained indefinitely if energy is continuously supplied.

48. How does the quality factor (Q factor) relate to damping in periodic motion?

The quality factor, or Q factor, is a dimensionless parameter that describes how underdamped an oscillator or resonator is. A higher Q factor indicates a lower rate of energy loss relative to the stored energy of the system. It's related to the sharpness of resonance and the rate at which oscillations decay. Systems with high Q factors resonate more easily and maintain oscillations for longer.

49. What is the role of potential energy curves in understanding periodic motion?

Potential energy curves provide a visual and mathematical representation of the forces acting on an oscillating system. The shape of the potential energy curve determines the nature of the motion. For simple harmonic motion, the curve is parabolic. Anharmonic oscillations have more complex curves. These curves help predict the motion, stable points, and energy levels of the system.

50. How do nonlinear oscillators exhibit behavior different from linear oscillators?

Nonlinear oscillators can exhibit a range of behaviors not seen in linear systems, including:

51. What is the significance of phase space in analyzing periodic motion?

Phase space is a graphical tool used to represent the state of a dynamical system. For periodic motion, it typically shows position versus velocity. In phase space:

52. How does the concept of natural frequency apply to different types of oscillating systems?

Natural frequency is the frequency at which a system tends to oscillate in the absence of driving or damping forces. It depends on the system's inherent properties:

53. What is the significance of Fourier analysis in studying complex periodic motions?

Fourier analysis is a powerful tool for understanding complex periodic motions:

54. How does the concept of impedance apply to periodic motion in different physical systems?

Impedance is a generalized concept that describes a system's opposition to motion or