The candle seesaw

A candle skewered transversely near its center of mass by a needle and balanced between two low-friction supports, when lit on both ends, will drip asymmetrically and begin to oscillate like a seesaw; these oscillations grow in time. We examine the onset of instability, and find that the candle does not oscillate quasi-stably until the vertical center of mass is lowered by the symmetrical melting of each end, creating a physical pendulum with a well-defined characteristic period. Additional asymmetric dripping below horizontal drives the pendulum, leading to linear growth in amplitude. The drop release becomes phase locked to the seesaw motion of the candle. We develop a small-angle analytical model that predicts the maximum growth rate when the dripping rate matches the seesaw frequency. Measurements of the motion, droplet phase, and melting rate confirm the validity of the model. We compare our results to earlier studies and make suggestions for the demonstrator.