How to Use the Hooke's Law Simulator
 

View & Orientation

• Use View to switch between Dark and Light mode.

• Use Orientation to hang the spring Vertically or lay it Horizontally. Vertical lets you add a hanging mass so gravity does the stretching. Horizontal removes gravity from the picture so you can focus only on the spring and the applied force.
   

Actions

• Press Release to let the spring move to its new position after you change a parameter. Press Reset to return the spring to its natural length.
   

Parameters

• Spring Constant (k) sets how stiff the spring is, in N/m. A larger k means a stiffer spring that stretches less for the same force.

• Turn on Add Mass to hang a mass from the spring. Set the Mass (m), and the simulator shows its Weight (Fg) and the Equilibrium position, where the spring force balances the weight.

• Gravity (g) changes the gravitational field strength, which changes the weight of the hanging mass.

• Applied Force (Fₐ) pushes or pulls on the end of the spring. Positive values stretch it and negative values compress it.
  Note for teachers: Have students predict the equilibrium stretch for a hanging mass using mg = kx before they turn on Add Mass. The Equilibrium readout gives them an instant check.
   

Calculated Values

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

• Notice that the spring force always points opposite the displacement. That is the negative sign in Fs = −kx.
   

Display

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

• Turn on the F vs. x Graph to watch the force-displacement relationship build as you change the applied force. The slope of that line is the spring constant.
  Note for teachers: Turning off most display elements gives you a clean picture of a spring for quick problem set or assessment images.
   

Challenge Mode (Test your understanding!)

• Difficulty: Easy or Hard. On Easy, you choose the input values, like the spring constant and the hanging mass. On Hard, the simulator picks random values and locks them, so you have to work with whatever spring you're given.

• A target position is shown (for example, Target: x = −0.70 m). Calculate the applied force needed to move the end of the spring to that position, rounded to the nearest whole newton.

• Enter your answer for Fa (N) and click Check. On Easy, use New target for another problem.
  Mastery tip: Before you calculate, decide whether the target is a stretch or a compression by comparing it to the Natural Length Marker. That tells you which direction your applied force needs to point.
   

Lab Mode

• In Lab Mode the spring constant is hidden. Your job is to find it from data.

• Hang a mass, choose the Value of g you want to use (9.8 N/kg or 10 N/kg), and the spring stretches to its new position right away.

• Click Record Data Point to log the mass, spring force, and stretch. Then change the mass and record again.

• Your independent variable is the mass (which sets the force on the spring), your dependent variable is the stretch, and the spring itself is your constant variable.

• Collect several data points and use the graph to determine the spring constant. Think about what the slope of a force vs. displacement graph represents.

• Use New lab (different spring) to start over with a new mystery spring.
  Mastery tip: Spread your masses out over a wide range. Points that are close together make it harder to get an accurate slope.