Masa Efectiva En Un Oscilador Armónico

Effective Mass of an Oscillating Spring
Eduardo E. Rodríguez, Gabriel A. Gesnouin,
Universidad de Buenos Aires and Universidad Favaloro, Buenos Aires Universidad Favaloro, Buenos Aires

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epresent an experimental method to obtain the effective mass of an unloaded oscillating spring. We measure the period T(n) of the partial springs that result when hanging n of the total N coils of agiven spring. Data are correlated with the expectation of a simple model for T(n) that takes into account the effective mass of the hanging spring. We analyze results for metal and plastic springs ofdifferent masses and strengths, and conclude that the method provides the effective mass with a good degree of reliability. A typical exercise in mechanics consists of finding the oscillation period T ofa mass m attached to the free end of a vertical spring of force constant k. If the mass mS of the spring is neglected, the period of free oscillations is1 (1) m T = 2p . k When the mass of the springis considered, a possibility is to write2
m + fmS (2) T = 2p , k where the term f mS, a fraction f of the spring’s mass mS, is the “effective mass of the spring,” and with its inclusion, the periodcorresponds to that of a mass m + f mS fastened to a massless spring. It is usual to obtain the effective mass by analyzing results of T(m) in the limit m ➝ 0.3 In this paper we present a newexperimental method to obtain the effective mass of an oscillating spring
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or, equivalently, the factor f. The method correlates the behavior of the partial springs formed when only n of the totalnumber N coils of a given spring are hanging and oscillating. First, we review some theoretical treatments that address the problem and afterward describe our experimental method derived from a simplemodel.

The problem
The problem of finding the value of f is approached in several texts by means of energy considerations,1 starting from the kinetic energy EK of an oscillating vertical spring of...