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Motion of a damped oscillating sphere as a function of the medium viscosity

In this paper, an experimental setup for undergraduate courses to study the damped harmonic motion of a sphere inside a fluid as a function of the medium viscosity is presented. To observe the dependence of the oscillation of the sphere on the medium viscosity, different concentrations of glycerin in water were used. The sphere is suspended on the end of a spring and its displacement is indirectly obtained using a force sensor. To describe the sphere motion, a drag force different from that given by Stokes' law is used. Our experimental results fit satisfactorily when semiempirical coefficients are introduced in the model. The frequency and relaxation time of the sphere oscillations diminish as the concentration of glycerin increases. Boundary effects due to the fluid container size are studied. We found that when the container size decreases the oscillations decay more rapidly due to a greater resistance to the motion of the sphere.