Presets
Playback
Right pan weights
Total mass on the right pan in grams (0.1 g steps).
Bob and bath
Raise the water bath so the bob is submerged.
Bob material
All bobs have the same volume, 28.3 cm3.
Bath liquid
Denser liquid means more buoyancy.
Beam
Centre of gravity depth d and knife-edge offset s set sensitivity and period.
Damper
Knife edges only, magnetic damper, or heavy oil dashpot.
Layers
Model checks
The science
Equation of motion
A beam of mass M, half-length L and centre of gravity d below the pivot carries two pans on knife edges a distance s below the pivot line. For beam angle θ (right end down) the torque balance is
I θ'' = g[ m_R (L cosθ − s sinθ) − m_L (L cosθ + s sinθ) ] − g M d sinθ − c θ'
with I = M L²/3 + (pan + load)(L² + s²). The left load is the bob minus the buoyant force: m_L = m_pan + ρV − ρ_f Vimm (with a quadratic drag correction). Stiffness K = g[(m_R + m_L) s + M d] gives the small-oscillation period T = 2π√(I/K), and the equilibrium tilt tan θ = L(m_R − m_L) / ((m_R + m_L) s + M d).
Archimedes
Weighing in air and in a liquid gives the density: ρ = ρ_f m_air / (m_air − m_liq). The 2D curve shows apparent mass against bath height: it falls linearly as the bob enters the liquid and flattens when fully submerged.
Honest simplifications: rigid beam, constant added mass ignored, drag modelled as a quadratic term while the bob is in the liquid, perfect knife edges, no surface-tension meniscus.
What to try
- Press the Iron in air preset and Release: the pointer overshoots, then settles at the equilibrium marker.
- Raise the bath: buoyancy takes mass off the left side and the equilibrium shifts.
- Press Auto-balance, then lower d: the curve in graph 2 gets steeper (more sensitive) and the period longer.
- Use the Mystery bob and compute its density from air and liquid balance weights.