Experimental study of simple harmonic motion of a spring-mass system as a function of spring diameter

The simple harmonic motion of a spring-mass system generally exhibits a behavior strongly influenced by the geometric parameters of the spring. In this paper, we study the oscillatory behavior of a spring-mass system, considering the influence of varying the average spring diameter Φ on the elastic constant k, the angular frequency ω, the damping factor γ, and the dynamics of the oscillations. It was found that the elastic constant k is proportional to Φ -3, while the natural frequency ω0 is proportional to Φ - 3 / 2, and γ decreases as Φ increases. We also show the differences obtained in the value of the angular frequency ω when the springs are considered as ideal (massless), taking into account the effective mass of the spring, and considering the influence of the damping of the oscillations. This experiment provides students with the possibility of understanding the differences between theoretical models that include well-known corrections to determine the frequency of oscillations of a spring-mass system.