Laplace System Builder
Laplace System Builder connects mechanical, spring, damper, integrator, gain and delay blocks and simulates their response in your browser.
Series chain · 1 of 6 blocks
1. Mass + spring + damper
1 / (1s² + 1s + 4)
Input → cascade → output
Y(s) = H(s) U(s)
Numerical time response with zero initial conditions. Values are shown in normalized teaching units.
Output at t = 0
Animated output · bounded display scale
At a glance
- Accepts
- Up to six series blocks; step, pulse or sine input; editable block parameters
- Outputs
- Transfer-function product, pole map, input/output graphs and an animated output
- Where it runs
- Entirely in your browser, on your device
- What leaves your device
- No calculation inputs are uploaded; standard site usage analytics still apply
- Limits
- Series cascades only; zero initial conditions; 12 time units; numerical simulation; normalized units
- Account
- Not required - there is no sign-up
- Price
- Free, with no watermark and no usage cap
- Made by
- Visrut
- Last updated
- 14 October 2026
What to notice
The mechanical block follows m x″ + b x′ + k x = force. Its transfer function is 1/(ms² + bs + k), assuming zero initial displacement and velocity. A standalone spring is static compliance 1/k; a standalone viscous damper has transfer 1/(bs).
Blocks form a series cascade: one output becomes the next input. Their transfer functions multiply. Reordering ideal linear time-invariant blocks preserves the exact cascade response, although numerical approximations may differ slightly.
A delay shifts the response; an integrator adds a pole at zero and can turn a steady input into an unbounded ramp. The moving tile represents the final output signal, not the physical displacement of every possible cascade.
Reference: University of Michigan system analysis tutorialFrequently asked questions
Does this upload my inputs?
The graphs and calculations run locally in your browser. There is no account or external calculation service.
Is this a symbolic Laplace calculator?
These are visual learning tools with causal presets, zero initial conditions and numerical simulations. They do not solve arbitrary symbolic expressions. Finite-window estimates are labelled separately from infinite-time transforms.