Modeling Bridge Oscillations Induced by Marching Soldiers

Abstract

This work simulates the effects of soldiers marching on a bridge, by first using Newton’s second law to write a differential equation describing the bridge's motion, and then solving the equation to yield a simple harmonic oscillator. Each of the soldiers’ steps is modeled as a constant impulse on the bridge. Computer simulations model the effects of between 5 and 200 soldiers marching both in and out of unison. We find that in both cases, the maximum amplitude of the oscillations of the bridge is proportional to the time the soldiers spent marching on the bridge. In the case where the soldiers march in unison, there is a linear relationship between the maximum amplitude of the oscillations and the number of marching soldiers. However, when the soldiers do not march in unison, the oscillations are proportional to the square root of the number of soldiers. Thus, it is preferable for soldiers to march out of unison on a bridge, since marching in unison could lead to a rapid increase in the amplitude of oscillations and the collapse of the bridge.