How to Use the Non-Linear Springs Simulator
 

View, Orientation & Actions

• Use View to switch between Dark and Light mode, and Orientation to set the spring Vertical or Horizontal.

• Press Release to let the spring move after you change a setting, and Reset to return it to its natural length.
   

Parameters

• Spring Constant (k) sets the overall strength of the spring.

• Power (n) sets how the force depends on displacement. Choose 0.5, 1, 1.5, 2, 2.5, or 3. The note under the selector tells you whether the spring stiffens or softens as it stretches.

• An n of 1 is an ideal Hooke's Law spring. Powers above 1 make the spring get stiffer the more you stretch it, and powers below 1 make it get softer.

• Applied Force (Fₐ) stretches or compresses the spring. Displacement is capped at ±3 m.
  Note for teachers: Real springs only behave linearly over a limited range. This simulator is a good way to show that Hooke's Law is a model with limits, not a universal rule.
   

Calculated Values

• This section gives a live readout of n, k, Displacement (x), Spring Force (Fs), and Applied Force (Fa).

• Try doubling the applied force and watch the displacement. With n = 1 the displacement doubles. With any other power it does not.
   

Display

• Use these toggles to choose what appears on the canvas: Displacement Indicator, Force Arrows, Equation Callout, Natural Length Marker, Equilibrium Marker, Coordinate Grid, and F vs. x Graph.

• Turn on the F vs. x Graph and compare different powers. A straight line means a linear spring. A curve that bends upward or downward tells you the power is above or below 1.
   

Challenge Mode (Test your understanding!)

• Difficulty: Easy or Hard.

• A target position is shown. Calculate the force at that position using Fs = k·xⁿ, rounded to the nearest whole newton.

• Enter your answer and click Check. Use New target for another problem.
  Mastery tip: Raise the displacement to the power first, then multiply by k. Doing it in the other order is the most common mistake.
   

Lab Mode

• In Lab Mode you get a mystery spring that follows Fs = k·xⁿ. Your job is to estimate both k and n from data.

• Stretch the spring to different displacements and click Record Data Point at each one to log the displacement and spring force.

• Your independent variable is the displacement, your dependent variable is the spring force, and the mystery spring is your constant variable.

• A graph of Fs vs. x will be curved, so you need to linearize it. Graph log(Fs) vs. log(x). The slope of that line is n, and the intercept gives you log(k).

• Use New mystery spring to start over with a different spring.
  Mastery tip: Before taking the logs, look at the shape of your Fs vs. x graph. It tells you whether n should come out above or below 1, which is a good check on your final answer.
  Note for teachers: This lab pairs well with log and log-log linearization in AP Precalculus. Students see the same technique in a physics context.