A point-absorber buoy is a damped, driven oscillator: the sea drives it at the wave period, a power take-off (PTO) system resists its motion (extracting energy as it does), and output peaks sharply when the wave period matches the buoy's own natural period — resonance.
z̈ + 2ζω₀ż + ω₀²z = F(t)/m (driven damped oscillator, ω₀ = 2π/T_natural)
P(t) = c_PTO · ż(t)² (instantaneous power ∝ damping × velocity²)
Peak output when T_wave ≈ T_natural (resonance)
- Wave height — bigger waves mean more driving force and more available power.
- Wave period — how fast the sea itself oscillates; compare it against the buoy's tuned period.
- Buoy natural period — the device's own resonant period, set by its mass and buoyancy — real converters are tuned or actively adjusted to chase this match.
- PTO damping — how hard the generator resists the buoy's motion; too little wastes motion, too much stalls it — there's an optimum.
Real-world relevance: this exact resonance-tuning problem is why most commercial wave-energy devices (like Ocean Power Technologies' PowerBuoy) actively adjust their PTO damping in real time as sea conditions change.