Mechanical Clock Escapement Simulator (2D)

This 2D companion to the 3D mechanical clock strips the mechanism down to the physics that actually keeps time: a pendulum whose period follows T = 2π√(L/g) releases the escapement one tooth at a time, and that escapement drives a gear train down to the clock face. Drag the pendulum-length slider away from the calibrated "seconds pendulum" length and watch the tick rate and the hands speed up or slow down together, while the live readout panel computes exactly how many seconds per day the clock would gain or lose at that length. The gear-ratio controls let you rebuild the train with a different escape-wheel tooth count and a different number of reduction stages, so you can see that changing the gearing changes the visual mechanism but never the clock's accuracy — only the pendulum's length does that.