Analyzing Oscillations on a Bridge


  • Newt Powers Chadwick School
  • Guillermo Goldsztein Georgia Institute of Technology



bridge, simple harmonic motion, oscillation, resonance, impulse


When people cross bridges, they create vibrations on these bridges because of the impulses they exert. In some cases, vertical oscillations have caused bridges to collapse due to a phenomenon called resonance. This paper utilizes simple harmonic motion to analyze the oscillations of bridges to create a mathematical model determining when certain bridges collapse. The paper first utilizes Hooke’s Law and Newton’s Second Law to create a second order differential equation of the motion of the bridge whose solution is a sine wave. Substituting in values for momentum for a singular impulse on the bridge, the paper then solves for the amplitude after the impulse. Adapting this model for impulses at different times and plotting the output graphs using Python, the bridge is shown to exhibit resonance and suggestions for damping are made.


Download data is not yet available.

Author Biography

Guillermo Goldsztein, Georgia Institute of Technology


References or Bibliography

Arioli, G., & Gazzola, F. (2015). A new mathematical explanation of what triggered the catastrophic torsional mode of the Tacoma Narrows Bridge. Applied Mathematical Modelling, 39(2), 901–912.

Barker, S. (2021, January 24). Every movie where the Golden Gate bridge has been destroyed. ScreenRant.

Billington, D. P. (1999, July 28). bridge. Encyclopædia Britannica.

Deshpande, Prachi Deepak. (2016). Understanding energy transfer in aeroelastic flutter and exploiting free-play induced flutter for energy harvesting. Graduate Theses and Dissertations, 15689.

García, E., Stadler, M., Larumbe, J., & García, F. (2003). Simple harmonic motion and damped oscillator. Acoustics Course.

Gou, H., Zhou, W., Bao, Y., Li, X., & Pu, Q. (2018). Experimental study on dynamic effects of a Long-span Railway Continuous beam bridge. Applied Sciences, 8(5), 669.

Khan Academy. (n.d.). What are momentum and impulse? (article). Khan Academy.

Lim, A. (2018, December 3). What is natural frequency? ThoughtCo.

Mishra, G. (2017, November 7). History of bridges - construction of bridges since ancient times. The Constructor.

Russell, D. A. (n.d.). Oscillation of a Simple Pendulum. Acoustics and Vibrations Animations.



How to Cite

Powers, N., & Goldsztein, G. (2021). Analyzing Oscillations on a Bridge. Journal of Student Research, 10(4).



HS Research Projects