A Sinusoidal Twist with Exponential Influences

Abstract

We show that the total distance traveled by an under-damped oscillating spring mass system with sinusoidal displacement results in a nice, closed-form expression.

Keywords:

• Spring mass system
• total displacement
• differential equation
• second-order
• geometric series
• signum function
• arc length
• hyperbolic function

Acknowledgements

I would to thank Dr. Brian Winkel for introducing me to SIMIODE and SCUDEM which opened up a whole new universe of materials and motivated some of this work. I would also like to thank the reviewers and editors for their recommendations which enhanced the exposition of this paper.

Additional information

Notes on contributors

Satyanand Singh

Satyanand Singh received his Ph.D. in mathematics from CUNY in 2014 and is interested in creating dynamic examples in mathematics that engages students and foster creativity. He was awarded the distinguished teaching award in 2017 from the MAA NY Metro section.