Mass-Spring-Damper Tutorial

In this quick tour, you will build and simulate a classic mass–spring–damper (SDOF) system and visualize the response, all in a few minutes.

Prerequisites

• Simit installed or access to the web workspace
• Basic familiarity with dynamic systems terminology

Goal

Model a unit mass attached to a spring and damper with an external force input, and observe displacement over time.

Parameters (editable later):

• m = 1.0 kg
• k = 50.0 N/m
• c = 0.8 N·s/m

1. Create a new model

• File → New Model → “MSD Quick Tour”
• Set simulation: step size dt = 0.002 s, duration T = 5 s

2. Add blocks

• Sources: Step (force input), initial value 0 → step to 1 N at 0.2 s
• Dynamics: Integrator (velocity), Integrator (position)
• Elements: Gain (−k), Gain (−c)
• Sinks: Scope (position)

Tip: Use / to open the palette and type to insert.

3. Wire the dynamics

The SDOF equations are ( m \dot v = F - kx - cv ), ( \dot x = v ).

• Sum forces: create a Sum block with inputs + + − −
  • Connect: F (Step) → +, k*x → −, c*v → −
• Compute k*x: position → Gain(−k) → Sum
• Compute c*v: velocity → Gain(−c) →

4. Set parameters

• Set gains: 1/m = 1.0, −k = −50.0, −c = −0.8
• Initial conditions: velocity(0) = 0, position(0) = 0

Optional via Console:

m = 1.0
k = 50.0
c = 0.8

Bind gains to variables 1/m, -k, and -c if your editor supports expressions or link fields to m,k,c as appropriate.

5. Run the simulation

• Press Run ▶; the position scope should show a lightly damped step response
• Use cursors to measure peak and settling time

6. Iterate quickly

• Change c to 2.0 (more damping) and re-run; compare curves
• Shorten dt to 0.001 s if the response looks jagged

Troubleshooting

• If signals blow up: check the 1/m, -k, -c signs and integrator connections
• If execution stops with a loop warning: ensure there is state (integrators) breaking algebraic cycles