Oscillatory motions. Frequency, period and resonance

22/04/2026

The online oscillatory motion simulations on this page will help you understand what these motions look like and under what circumstances they can be generated.

This Thematic Unit is part of our Physics collection

Amplitude

Maximum displacement value of an oscillating body relative to its equilibrium position.

Angular Frequency

Measure of the rotation rate or the rate of change of the motion’s phase, expressed in radians per second (rad/s).

Elongation

Distance or angle that separates the oscillating body from its equilibrium position at a given instant.

Frequency

Number of complete turns or revolutions an object makes in a given unit of time.

Oscillation

Repetitive back-and-forth motion of a body passing through an equilibrium position.

Period

Time required for an object in circular motion to complete one full revolution or turn.

Phase

State of vibration of a particle at a given instant, defined by the angle that determines its position and direction of motion.

Simple Harmonic Motion

Periodic back-and-forth motion in which a body oscillates about an equilibrium position under the action of a restoring force.

Simple Pendulum

Idealized model consisting of a point mass suspended from an inextensible, weightless string.

What are oscillatory motions

Oscillatory motions are a type of motion that occurs when an object moves repetitively around an equilibrium position. This type of motion is very common in nature and technology, and can be observed in a wide variety of systems, from the pendulum of a clock to sound waves traveling through the air.

Characteristics of oscillatory motions

Oscillatory motion is characterized by the presence of a restoring force that acts on the moving object and returns it to its equilibrium position. This force can be of different nature such as gravitational in the case of the pendulum, or electrical or magnetic in the case of oscillatory circuits.

Importance of oscillatory motions

This type of motion is very important in physics, engineering and technology. For example, it is used in the manufacture of clocks and stopwatches, in the construction of suspension bridges and in the transmission of radio signals. It is also fundamental in the understanding of concepts such as kinetic energy, potential energy and conservation of energy.

Frequency and period of oscillatory motion

Frequency is defined as the number of complete oscillations an object makes in one second. The unit of measurement for frequency is the Hertz (Hz). Period is defined as the time it takes for an object to make one complete oscillation. It is measured in seconds (s) and is the inverse of frequency. The mathematical relationship between frequency and period is expressed as:

frequency = 1 / period

Frequency and period are determined by the magnitude of the restoring force and the mass of the moving object. Frequency and period are two very important measurements in the study of oscillatory motion, since they describe the repetition of the motion and allow to calculate the velocity and acceleration of the moving object.

Resonance of oscillatory motion

When the frequency of the external force applied to a system coincides with the natural frequency of oscillation of the system, the phenomenon of resonance occurs. In this case, the moving object absorbs energy from the external force and its oscillation amplitude increases significantly. This phenomenon can be observed in many systems, from mechanical oscillators to electronic circuits.

In short, the online oscillatory motion simulations on this page help us to better visualize and understand this important type of motion.

Amplitude

Maximum displacement value of an oscillating body relative to its equilibrium position.

Angular Frequency

Measure of the rotation rate or the rate of change of the motion’s phase, expressed in radians per second (rad/s).

Elongation

Distance or angle that separates the oscillating body from its equilibrium position at a given instant.

Frequency

Number of complete turns or revolutions an object makes in a given unit of time.

Oscillation

Repetitive back-and-forth motion of a body passing through an equilibrium position.

Period

Time required for an object in circular motion to complete one full revolution or turn.

Phase

State of vibration of a particle at a given instant, defined by the angle that determines its position and direction of motion.

Simple Harmonic Motion

Periodic back-and-forth motion in which a body oscillates about an equilibrium position under the action of a restoring force.

Simple Pendulum

Idealized model consisting of a point mass suspended from an inextensible, weightless string.

Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!

Oscillatory motion simulations

Horizontal oscillation without energy loss

Horizontal oscillation without energy loss II

This simulation is another example of horizontal oscillatory motion without energy loss. Vary the parameters, move the mass horizontally and see what the motion looks like.

Horizontal oscillation with energy loss

Vertical oscillation

Vertical Oscillation II

This simulation is another example of vertical oscillatory motion without energy loss. Vary the parameters and see what the motion looks like.

Resonance

In the last of these online oscillatory motion simulations, resonance will be studied. Resonance is a phenomenon in which the amplitude increases at a given frequency. The phenomenon of resonance can be easily observed all around us.

Normal Modes

Dive into the dynamics of coupled oscillator systems with this Normal Modes simulation. Explore one-dimensional and two-dimensional configurations by adjusting the number of masses and initial conditions, and observe how different normal modes emerge with their characteristic frequencies, amplitudes, and phases. Identify which modes are present, understand why those with higher indices vibrate faster, and discover how any complex motion can be decomposed using the principle of superposition.

Giants of science

“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Johannes Kepler

1571

–

1630

Kepler formulated the three laws of planetary motion, establishing elliptical orbits and the relationship between planetary period and distance from the Sun

“The heavens teach the geometry that nature follows”

Joseph-Louis Lagrange

1736

–

1813

Joseph-Louis Lagrange formulated the Lagrangian equations, key in classical mechanics to describe motion. He also founded variational calculus, applying it to algebra and mathematical physics

“As soon as a mathematical truth is established, it always serves as a starting point for new truth”

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Galileo Galilei

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1642

Galileo Galilei revolutionized astronomy by observing planets, Jupiter’s moons, and advocating heliocentrism.

“And yet it moves”

Augustin-Louis Cauchy

1789

–

1857

Augustin-Louis Cauchy formalized mathematical analysis, providing rigor to calculus and function theory, influencing mathematical physics

“Rigor in mathematics is the key to understanding physical phenomena”

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Test your knowledge

What characterizes an oscillatory motion, and why is it a fundamental model for describing physical systems that repeat over time?

Oscillatory motion is defined as the periodic movement of a system around an equilibrium position under the action of a restoring force. This restoring force always points toward the equilibrium and increases as the system moves farther away from it, creating a continuous cycle of displacement, return, and overshoot. Oscillatory motion is fundamental because it appears in an enormous variety of physical systems: springs, pendulums, vibrating molecules, electrical circuits, and even waves. It provides a framework for understanding stability, energy exchange, resonance, and how systems respond to disturbances. Many complex phenomena can be reduced to or approximated by oscillatory models, which makes them central in physics and engineering.

How do mass, system stiffness, and amplitude influence the frequency and energy behavior of an oscillation?

The frequency of an oscillation depends on the intrinsic properties of the system. In a mass‑spring system, a larger mass lowers the frequency, while a stiffer spring increases it. In a pendulum, the determining factor is the length: longer pendulums oscillate more slowly. Although amplitude does not affect frequency in ideal oscillators, it does determine the total energy of the motion. Larger amplitudes correspond to greater potential and kinetic energy throughout the cycle. These relationships allow us to predict how the system evolves, how it reacts to external forces, and under what conditions the oscillation remains stable or becomes damped.

Why do a spring or a pendulum always “come back” to the center? What forces them to return again and again?

They return because of the restoring force. When the system is displaced from equilibrium, a force appears that pushes it back toward the center. The farther it moves, the stronger that force becomes. As the system accelerates toward equilibrium, inertia carries it past the center, and then the restoring force pulls it back again. This constant interplay between inertia and restoration is what creates the repetitive motion.

How come the oscillation doesn’t stop immediately when there is friction? Shouldn’t it lose energy right away?

Friction does remove energy, but it does so gradually, not instantaneously. Each cycle loses a small portion of energy, which reduces the amplitude little by little. That’s why the motion fades smoothly instead of stopping abruptly. Only in a perfectly frictionless system—an idealization—would the oscillation continue forever without losing amplitude.

Why does the frequency of a pendulum depend on its length and not on its mass? Doesn’t the weight matter?

In a simple pendulum, mass doesn’t affect the frequency because both the restoring force and the inertia scale proportionally with mass. They cancel each other out. What does matter is the length: it determines the arc of motion and the angular acceleration. A longer pendulum takes more time to complete each swing, while a shorter one oscillates faster. That’s why pendulum clocks adjust their timing by changing the length, not the weight.