Physics Simulator

Explore classic mechanics interactively. Drag inside the stage to aim or set up each system, adjust the parameters, and watch the motion play out in real time. Everything runs locally in your browser.

How It Works

This simulator numerically integrates the equations of motion for three classic mechanical systems. Distances on screen are scaled from meters, and time advances in small steps each animation frame, so the motion you see reflects the physics of the parameters you choose.

Projectile Motion

A projectile launched at speed v and angle θ follows a parabolic path under constant gravity. With no air resistance the key results are:

• Range: R = v² · sin(2θ) / g
• Maximum height: H = v² · sin²(θ) / (2g)
• Time of flight: T = 2v · sin(θ) / g

The maximum range on level ground occurs at a launch angle of 45°. Enabling air resistance adds a drag force proportional to velocity, which shortens the range and makes the path asymmetric. Mass only affects the trajectory when air resistance is turned on. without drag, all masses fall together.

Simple Pendulum

A pendulum swings under gravity about a pivot. This simulator integrates the full non-linear equation α = −(g / L) · sin(θ), so large swings behave realistically. For small angles the period simplifies to T = 2π√(L / g), which depends on length and gravity but not on mass. Add damping to model air friction and watch the amplitude decay.

Mass on a Spring

A mass on a spring obeys Hooke's law, F = −k · x, producing simple harmonic motion with period T = 2π√(m / k). A stiffer spring (larger k) oscillates faster; a heavier mass oscillates slower. Gravity sets the resting position but not the period. The damping control removes energy each cycle so the oscillation gradually settles at equilibrium.

Tips

• Drag directly inside each stage to aim the launcher, pull the pendulum bob, or stretch the spring.
• Change sliders while a simulation runs to see the effect instantly.
• Use the projectile Clear button to wipe old trails and compare launches side by side.