Equilibrium
Two opposing forces, one point where they cancel. The shape underneath the pendulum, the falling raindrop, and the optimal portfolio: name the forces, write the balance equation, solve for where the net change vanishes.
the skeleton
- 1 two opposing forcesIdentify what pushes the system one way and what pushes it back.
- 2 balance equationWrite the net force / net rate as a single algebraic expression.
- 3 fixed pointSet the net to zero and solve for the state where nothing changes.
instances · 3
physics · pendulum-clock
The Pendulum Clock
objective gravity restoring force vs angular displacement
stops when θ̈ = −(g/L) sin θ — linearised to a single fixed frequency.
physics · terminal-velocity
Why Falling Stops Speeding Up
objective gravity pulling down vs drag pushing up
stops when dv/dt = g − kv → set to 0 → v_t = g/k.
physics · damped-oscillator
Why Things Stop Swinging
objective restoring force vs damping force
stops when Equilibrium at the origin; the damping ratio decides how it gets there.
leans on
walk the instances
Where Change Vanishes →
One question — *where does change vanish?* — under three physics applications.