Spring Constant Simulator
Interactive Hooke's Law visualization with spring compression and extension
About this Simulator
Experience Hooke's Law firsthand! Drag the mass to stretch or compress the spring and watch the force-displacement relationship in real-time. The F-x graph shows the linear relationship characteristic of ideal springs, while color changes indicate stress levels in the spring wire.
Physics & Formulas
Hooke's Law:
$$F = k \cdot x$$
Spring Constant (Helical Spring):
$$k = \frac{G d^4}{8 D^3 n}$$
Potential Energy:
$$U = \frac{1}{2} k x^2$$
How to Use
- Drag the mass up or down to apply force and see displacement
- Use the Applied Force slider for precise force control
- Adjust Spring Constant to see how stiffer springs deflect less
- Watch the F-x graph update in real-time showing the linear relationship
- Enable Stress Color to see the spring change color under load
- Click Oscillate to see the spring in harmonic motion
- Note: Negative force compresses the spring, positive extends it
Frequently Asked Questions
What is the spring constant (k)?
The spring constant represents stiffness - how much force is needed to stretch or compress the spring by a unit distance. Higher k means a stiffer spring. Units are N/m or lb/in.
When does Hooke's Law not apply?
Hooke's Law is only valid in the elastic region. If you exceed the elastic limit, the spring deforms permanently (plastic deformation). The stress color indicator turns red as you approach this limit.
How is spring constant related to geometry?
For helical springs: k = Gd⁴/(8D³n), where G is shear modulus, d is wire diameter, D is coil diameter, and n is number of active coils. Thicker wire or tighter coils increase stiffness.
What determines the stored energy?
Potential energy U = ½kx². This means energy increases with the square of displacement - double the stretch stores four times the energy. This is why springs can store and release energy efficiently.
