Various simulations of small physical systems, using RK4 to integrate equations of motion obtained using Lagrangian mechanics.

pendulum + spring - mass on a spring attached to a cart moving on a horizontal rail (most advanced)
inverted pendulum balacing with ML - balancing a rod on a movable cart
pulley - two masses, one swinging, hanging from a string wrapped around a pulley
pendulum - pendulum + spring but without the springy part