Resonance in an Undampened Spring-Mass System

by Blair Gramentz

Submitted : Fall 2009

A mass is attached to a spring suspended from the ceiling. If a force is applied to this system and released, the spring will oscillate at its natural frequency. Consider an intermittent force applied to this system which varies in frequency. How will these forces affect the preferred frequency of the spring? What impact does this have on the oscillation of the system? This experiment was conducted using differential equations and Euler integration in Microsoft Excel. An understanding of differential equations and Euler integration was critical in order to calculate the data. Since the preferred frequency of the spring system would ultimately characterize the oscillation of the system, the natural frequency was calculated prior to the experiment. Once the differential equations, Euler integration, and the preferred frequency were all accounted for, formulas were entered into Microsoft Excel to fully characterize the position and velocity for any time and for any driving frequency.

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