Investigating t∞ for bouncing balls

Abstract

A simple experiment carried out with readily available equipment is used to investigate the interesting physics that occurs when a ball is bounced on a flat surface and left to continue bouncing until it stops. A solution well known from introductory physics courses is that if a ball loses a fraction of its energy on each bounce, then it will bounce infinitely many times in a finite time interval. A convolutional model of the sound a bouncing ball makes is created using an impulse response function and a prediction based on energy loss that the sound amplitudes will decay linearly to zero as the ball stops bouncing. Strategies for data analysis using correlation and deconvolution with the impulse response function are shown to simplify the picking of bounce times. Observations from several data examples show that the convolutional model is a good description of the real data and that we observe a linear decrease in sound amplitude consistent with the model prediction.