Physics Lab

Three live simulations: a projectile with air drag, a damped oscillator with its eigenvalues, and the exact period of a pendulum.

Projectile with air drag

Damped oscillator

Pendulum: exact period

v˙=g−ρCDA2m∣v∣ v\dot{\mathbf v}=\mathbf g-\frac{\rho C_DA}{2m}|\mathbf v|\,\mathbf v
s=−ζωn±ωnζ2−1s=-\zeta\omega_n\pm\omega_n\sqrt{\zeta^2-1}
T=2πℓ/gAGM⁡(1,cos⁡θ02)T=\frac{2\pi\sqrt{\ell/g}}{\operatorname{AGM}(1,\cos\frac{\theta_0}{2})}

Generic, illustrative values. Same methods as the math page: RK4 with Δt = 1 ms for drag at sea-level density 1.225 kg/m³, the characteristic equation for the oscillator, and the arithmetic–geometric mean for the exact pendulum period.

Learn the math behind each number

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