Understanding Hooke’s Law — Free Interactive Simulator
Hooke’s Law is one of the foundational principles in physics and mechanical engineering. It states that the force needed to extend or compress a spring is directly proportional to the displacement from its natural length: F = kx. The constant k is the spring constant (or stiffness), measured in N/m. This law holds within the elastic limit — beyond that, permanent deformation occurs and the relationship becomes non-linear.
Force-Extension Graphs & Energy
A force-extension graph for a spring obeying Hooke’s Law is a straight line through the origin with gradient k. The area under the graph equals the elastic potential energy stored: Ep = ½kx². This energy can be fully recovered when the spring returns to its natural length (within the elastic limit). The simulator above lets you see this energy area grow in real time as you increase the load.
Series & Parallel Spring Combinations
When springs are placed in series (end to end), the effective spring constant is lower than either individual spring: 1/keff = 1/k1 + 1/k2. In parallel (side by side), the stiffness adds up: keff = k1 + k2. Toggle between configurations in the simulator to see the difference in extension for the same load.
How to Use This Tool
In Simulate mode, drag the weight or use the sliders to apply force to the spring. Watch the force-extension graph plot in real time, and see the energy stored. Switch to Explore mode to study 12 key concepts with formulas, diagrams, and worked examples. Practice mode generates random problems, and Quiz mode tests your understanding with 5 questions per session.