Oscillation of Bridge: Mathematical Modeling of the Amplitude Under Different Situations

Abstract

We consider a function that shows the position of a bridge. This function includes the effect of the force applied by the soldier marching on it. We analyze the function and obtain how the impulse effect the position of the bridge in different cases, such as the resonance case-when the soldier applies a force with the same frequency as the frequency of the bridge oscillations-and the non-resonance case-when the soldier applies a force with a different frequency from the frequency of the bridge oscillations.