Physics — STUDiiO

← LABPHYSICS / SOFTWARE / LIGHT EXPERIMENT

FORM / MOTION / LIGHTStill studies

Z DEPTH 1.00× SPIN 1.00× LIGHT 0°

Newton’s second law

ODE

m \frac{d^{2} x}{d t^{2}} = F

Force sets the acceleration.

ODE

\frac{d}{d t} (\frac{\partial L}{\partial \dot{q}}) - \frac{\partial L}{\partial q} = 0

The path of stationary action.pendulum: angle vs angular speed

ODE

\frac{d^{2} x}{d t^{2}} = - ω^{2} x

Restoring force: pure oscillation.

ODE

m \frac{d^{2} x}{d t^{2}} + b \frac{d x}{d t} + k x = 0

Friction drains the swing away.

ODE

\frac{d N}{d t} = - λ N

Rate of decay ∝ amount left.

PDE

\frac{\partial^{2} u}{\partial t^{2}} = c^{2} \nabla^{2} u

Disturbances travel at speed c.

PDE

\frac{\partial u}{\partial t} = α \nabla^{2} u

Hot spots spread and smooth out.

PDE

\nabla^{2} φ = - \frac{ρ}{ε_{0}}

Charges set the potential.

PDE

\nabla \times E = - \frac{\partial B}{\partial t}

Changing B makes E circulate.

PDE

i ℏ \frac{\partial ψ}{\partial t} = \hat{H} ψ

How a quantum state evolves.

PDE

ρ (\partial_{t} v + (v \cdot \nabla) v) = - \nabla p + μ \nabla^{2} v + f

\nabla \cdot v = 0

Newton’s second law for a fluid.

PDE

G_{μ ν} + Λ g_{μ ν} = \frac{8 π G}{c^{4}} T_{μ ν}

Mass-energy curves spacetime.