How to Use the Spring Systems Simulator
 

View

• Use View to switch between Dark and Light mode.
   

Configuration

• Use Mode to connect the springs in Series (end to end) or in Parallel (side by side).

• Choose the Number of Springs, from 1 to 5. A spring constant slider appears for each one.
  Note for teachers: Start with one spring so students see the baseline, then add a second identical spring in each mode. Series makes the system softer and parallel makes it stiffer, and most students predict this backwards.
   

Orientation & Actions

• Use Orientation to set the system Vertical or Horizontal.

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

Spring Constants

• Set each spring's constant (k1, k2, and so on) in N/m.

• Applied Force (Fa) stretches or compresses the whole system. Positive values stretch and negative values compress.
   

Calculated Values

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

• Change one spring's constant and watch how keff responds. In series, keff is always smaller than the weakest spring. In parallel, keff is the sum of all of them.
  Mastery tip: Calculate keff yourself before you look. For series use 1/keff = 1/k1 + 1/k2 + …, and for parallel use keff = k1 + k2 + ….
   

Display

• Use these toggles to choose what appears on the canvas: Displacement Indicator, Force Arrows, keff Formula, Individual Spring Labels, F vs. x Graph, and Coordinate Grid.

• The keff Formula shows the calculation for the current configuration, which is a helpful check while you are learning the two rules.
  Note for teachers: Springs combine the opposite way from resistors. Springs in series add like resistors in parallel, and springs in parallel add like resistors in series. This is a nice connection to make later when you teach circuits.
   

Challenge Mode (Test your understanding!)

• Difficulty: Easy or Hard. On Hard the keff readout is hidden, so you must calculate it from the individual spring constants first.

• A target position is shown. Calculate the applied force needed to move the system to that position, rounded to the nearest whole newton.

• Enter your answer for Fa (N) and click Check.
  Mastery tip: Treat this as a two-step problem. Find keff first, then use Hooke's Law with keff as if the whole system were one spring.
   

Lab Mode

• In Lab Mode the individual spring constants are hidden. The panel tells you how the springs are connected (for example, "This system has 2 springs in series") and asks you to find keff.

• Drag the end of the system on the canvas to stretch or compress it, then click Record Data Point to log the displacement and spring force.

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

• Record several points across a wide range of displacements, then use the slope of your force vs. displacement graph to determine keff.

• Use New lab (different spring system) for a new mystery system.
  Mastery tip: Once you know keff, see if you can work backward. If the springs are identical, what must each individual spring constant be?