The Hooke’s Law simulation from PhET lets you stretch and compress springs to explore how force, spring constant, displacement and potential energy are related. You can also connect two springs in series and in parallel and see how this changes the effective spring constant. It is free, runs in any browser on a phone, tablet or laptop, and it is a great fit for the elasticity, force and work and energy lessons in Tamil Nadu State Board (Samacheer Kalvi) Physics.
What is the Hooke’s Law simulation?
This interactive simulation lets you pull and push on a spring and see the force, the displacement and the stored energy. You can change the spring constant, and you can also connect two springs in series or in parallel. Because it runs on HTML5, there is nothing to install, and it works on phones, tablets, Chromebooks and computers.
High school and university
Springs, force, spring constant and potential energy
Phone, tablet, Chromebook, PC
English
PhET’s learning goals are to explain the relationships among applied force, spring force, spring constant, displacement and potential energy, to describe how connecting two springs in series or in parallel changes the effective spring constant, and to predict how the stored energy changes with the spring constant and the displacement.
Launch the Hooke’s Law simulation online
Tap or click inside the player and start exploring. Use the full-screen button in the player for a bigger view.
Credit: University of Colorado Boulder
How to use the Hooke’s Law simulation, step by step
- Predict first. Before you stretch the spring, say what will happen to the force when you stretch it twice as far.
- Stretch and compress. Pull and push the spring and watch the force and the displacement.
- Change the spring constant. Try a stiffer and a softer spring and compare the force at the same displacement.
- Look at the energy. Watch how the potential energy stored in the spring changes with the displacement.
- Connect two springs. Try a series and a parallel arrangement and compare the effective spring constants.
Tip for students: record the displacement and the force in a table, then plot a graph. The points fall on a straight line.
The idea behind the simulation: F = kx and PE = ½kx²
F = k × x, PE = ½ × k × x²
Here F is the spring force in newtons (N), k is the spring constant in N/m, x is the displacement from the rest length in metres and PE is the stored potential energy in joules (J). A stiffer spring has a bigger k. For two springs, the effective spring constant is k₁ + k₂ in parallel, and (k₁ × k₂) ÷ (k₁ + k₂) in series.
Worked example: A spring with k = 200 N/m is stretched by 0.10 m. The force is 200 × 0.10 = 20 N, and the stored energy is ½ × 200 × 0.10² = 1 J. If you stretch it twice as far, to 0.20 m, the force doubles to 40 N but the energy becomes four times as big, 4 J.
Spring key terms explained
These are the words you will meet while using the Hooke’s Law simulation, with simple meanings.
Hooke’s law
The force a spring exerts is proportional to how far it is stretched or compressed.
Spring constant (k)
A measure of how stiff the spring is, in N/m. A bigger k means a stiffer spring.
Displacement (x)
How far the spring is stretched or compressed from its rest length.
Spring force
The restoring force of the spring. It pulls or pushes back toward the rest length.
Applied force
The force you use to stretch or compress the spring.
Potential energy
The energy stored in a stretched or compressed spring.
Series
Two springs connected end to end, one after the other.
Parallel
Two springs connected side by side, sharing the load.
Common mistakes: Using centimetres instead of metres in F = kx, thinking that doubling the stretch doubles the energy (it makes it four times as big), and mixing up the series and parallel formulas.
Try the spring calculator (practice what you explore)
Enter the spring constants, choose how the springs are connected, and set the displacement. The calculator gives the effective spring constant, the force and the stored energy. Then tap a “what if” button.
What happens when you change a variable
| Change | Effect |
|---|---|
| Double the displacement | The force doubles and the energy becomes 4 times as big |
| Stiffer spring (bigger k) | More force and more energy at the same displacement |
| Two springs in parallel | The effective spring constant is k₁ + k₂ (stiffer) |
| Two springs in series | The effective spring constant is smaller than either spring (softer) |
| Compress instead of stretch | The force reverses direction, the energy is the same |
Classroom activities for teachers
The Hooke’s Law simulation fits a single 40-minute period.
- Predict and test (10 min): students predict the force at a new displacement, then check.
- Force graph (10 min): students record force against displacement and find the spring constant from the slope.
- Series and parallel (10 min): students compare the effective spring constants for the two arrangements.
- Exit ticket (10 min): students explain in two sentences why doubling the stretch makes the energy four times as big.
Looking for the matching chapters? Browse the Science and Physics books on TN SchoolBooks and download the Samacheer Kalvi PDFs, then use this simulation to make the elasticity and energy lessons visual. More free science simulations and textbook PDFs are on the home page.
Quick quiz: test your understanding of springs
Score: 0 / 5
Hooke’s Law simulation: frequently asked questions
Is the Hooke’s Law simulation free?
Yes. PhET simulations are free to run online in a browser. Check PhET’s licensing page for reuse terms.
Does it work on a mobile phone?
Yes. It is built with HTML5 and works on phones, tablets and Chromebooks. Use landscape mode or the player’s full-screen button for a bigger view.
What does Hooke’s law say?
Hooke’s law says that the force a spring exerts is proportional to its displacement from the rest length, F = kx. It holds as long as the spring is not stretched past its elastic limit.
What is the effective spring constant for springs in series and in parallel?
In parallel it is k₁ + k₂, which makes a stiffer spring. In series it is (k₁ × k₂) ÷ (k₁ + k₂), which makes a softer spring.
The Hooke’s Law simulation turns an invisible force into something you can stretch, measure and graph. Explore it, take the quiz above, and keep experimenting until predicting a spring’s force and energy feels easy.