Normal Modes: Coupled Oscillators
Drag masses on springs, excite each normal mode and see how every motion is a mix of modes.
Drag the masses up and down to start any motion, or press a mode button. Every motion is a mix of normal modes, each with its own frequency.
About the Normal Modes: Coupled Oscillators
Free normal modes: coupled oscillators. Drag masses on springs, excite each normal mode and see how every motion is a mix of modes. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for physics, the normal modes: coupled oscillators runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Drag masses on springs, excite each normal mode and see how every motion is a mix of modes. Use it to explore physics ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Normal Modes: Coupled Oscillators
- Use the controls to change Masses, Excite a mode, Damping. The simulation reacts instantly.
- Pick an option such as 3 masses, 5 masses, 7 masses to switch modes or load an example.
- Press "Stop motion" to start, reset or change what is happening.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Excite mode 1, then mode 3.
- Pull a single mass and watch the energy bars.
- Change to 7 masses.
Key ideas you can learn
- Each normal mode has one frequency and a fixed shape.
- Any motion is a sum of normal modes.
- Higher modes have more nodes and higher frequency.
- Energy is shared between modes.
Where this is used in the real world
Engineers study normal modes to stop bridges and buildings from resonating.
Who is this simulation for?
Physics students in middle school, high school and first-year university, teachers who want a quick demonstration for the projector, and anyone revising for exams. It works well for flipped classrooms because students can explore before the lesson.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
What is a normal mode?
A pattern of motion in which all parts move at the same frequency.
Why are normal modes important?
They split a complicated vibration into simple parts, used for bridges, molecules and musical instruments.
Is the Normal Modes: Coupled Oscillators free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Normal Modes: Coupled Oscillators work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.