Analytical and Experimental Study of a Variable-Mass Oscillator with Constant Mass Loss

RESUMO

We present an analytical and experimental study of a variable-mass oscillator with constant mass loss. Starting from the equation of motion of a spring-mass system whose mass decreases linearly with time, analytical solutions are obtained in terms of Bessel functions. Simple asymptotic expressions are then derived, providing explicit descriptions of the evolution of the oscillation amplitude and frequency. The analysis is extended to include viscous damping, leading to a model suitable for direct comparison with experimental observations. Experimental measurements of the oscillator acceleration were performed using a simple laboratory setup consisting of a spring-mounted container that continuously loses mass at an approximately constant rate. The theoretical predictions accurately reproduce the measured dynamics over the entire duration of the oscillation, and the massloss rates obtained from the fits are in good agreement with independent measurements. The results provide an accessible example of variable-mass dynamics and illustrate how special-function methods can yield experimentally testable predictions in advanced undergraduate mechanics.