Simulations

Projectile Lab

Launch a projectile and watch range, apex height and time of flight update live — with or without air resistance.

Pendulum Lab

Release a pendulum and watch it swing in real time — change length, gravity and damping, and see how the real period drifts from the small-angle formula at big amplitudes.

Linear Algebra Lab

Drag the four entries of a 2×2 matrix and watch the grid transform — basis vectors, determinant as area scale, and eigenvector directions, all live.

ODE Phase Lab

Drag the four entries of a 2×2 system ẋ = Ax and watch the phase portrait reshape — slope field, a live trajectory and a stable node / saddle / spiral / centre verdict from the eigenvalues.

Mohr's Circle Lab

Set σx, σy and τxy and watch Mohr's circle, the principal stresses and the max shear update — then rotate the plane and see the point travel the circle.

Stress-Strain Lab

Pull a virtual specimen and trace its stress-strain curve through elastic, yield, hardening, necking and fracture — for steel, aluminium, copper, titanium or cast iron.

Ashby Materials Lab

Pick the best material for the job on a modulus-vs-density chart — choose tie, beam or panel and sweep the index guideline to see why wood and CFRP beat steel.

Mass Balance Lab

Solve a process flowsheet with a recycle loop — drag the feed and split fractions and watch every stream flow update, all balanced simultaneously.

Heat Transfer Lab

Heat a rod's ends and watch the temperature profile relax toward the steady gradient — a live finite-difference solution of the heat equation.

Beam Lab

A simply-supported beam with a movable point load and an optional distributed load — watch the shear and bending-moment diagrams and the deflected shape update live.

Truss Lab

Load a Warren truss and watch every member light up — green for tension, amber for compression — with the real forces solved by the method of joints.

Pipe Flow Lab

Push water through a pipe and find your operating point on the Moody chart — drag velocity, diameter, length and wall roughness and watch the Reynolds number, flow regime and head loss respond.

Slope Stability Lab

Will the hillside slide? Drag the slope angle, soil cohesion and friction and watch the slip circle, the sliced failure mass and the factor of safety update — with a stable / marginal / unstable verdict.

Bridge Builder Lab

Will your bridge hold? Pile a load onto the deck and the truss is solved member-by-member, each rated against its strength — the most-stressed member turns red and fails first, with a live holds / collapses verdict.

Circuit Lab

A loaded voltage divider you can tune — change the source and the resistors and watch the node voltage, branch currents and power update, solved by real nodal analysis.

Logic Gate Lab

Wire two logic gates as (A op B) op C, toggle the inputs and watch the signals light up — with the full truth table filling in live.

Bode Filter Lab

Drag R and C on a first-order RC filter and watch the Bode magnitude and phase plots respond — with the −3 dB corner frequency marked.

Fourier Lab

Build a square, sawtooth or triangle wave out of pure sine waves — pull the harmonics slider and watch the partial sum sharpen toward the target, Gibbs overshoot and all.

Smith Chart Lab

Drag a normalized impedance and watch its point move on the Smith chart — with |Γ|, VSWR and return loss live, and your constant-VSWR circle drawn.

Moment of Inertia Lab

Resize an I-beam cross-section and watch its area, centroid, second moments of area and section modulus update — the parallel-axis theorem, made visual.

Column Buckling Lab

Load a column to its buckling limit — set length, diameter, material and end conditions and watch the critical load and the Euler ↔ Johnson regime update on the design curve.

Vibration Lab

Drive a damped system near its natural frequency and watch resonance blow up — drag ζ and the frequency ratio to trace the magnification (and transmissibility) curve.

Gear Train Lab

Mesh a driver and driven gear (with an optional idler) and watch them spin at their true relative speeds — with the gear ratio, output rpm, torque multiplier and direction live.

Thermo Cycle Lab

Trace the ideal Otto cycle on a P–V diagram — change the compression ratio and heat input and watch the work loop and thermal efficiency respond.

Four-Bar Linkage Lab

Set the four link lengths and watch the linkage move — a crank-rocker spins, a non-Grashof one only rocks — with the coupler curve traced live.

Control Loop Lab

Drag the damping ratio and natural frequency of a second-order system and watch its step response — overshoot, settling and ringing — change in real time.

Root Locus Lab

Turn up the feedback gain and watch the closed-loop poles travel the s-plane — meet, break away and split into a complex pair — with damping and stability live.

Queue Lab

Watch a single-server queue fill up — set the arrival and service rates and a live M/M/1 simulation animates the line while the utilisation, average length and wait update. Push it past capacity and the queue explodes.