Abstract

Citation

Researchers should cite this work as follows:

• Ahlstrom, E., Singh, S., John Sieben, Fogarty, T., Thoo, J. (2022). 3-090-OneSpringMass-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/TBGB-TA07

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Article Context

Description

We see a bob hanging from a spring vertically, and below it is a motion detector that was used to collect data (vertical position of the bob and time) for the motion of the bob. This data was then compared against the mathematical model for the motion.

After either raising the bob or pulling it down from its rest position or static equilibrium, and then letting go, it moves up and down like clockwork. Let us assume that there are only two forces acting on the bob: the force that is due to gravity and the force produced by the spring. We will not assume there is resistance force. The force that is due to gravity is given by mass*gravity ( m g ), and the force produced by the spring is proportional to the amount (length) that the spring has been stretched or compressed (k x )) from its rest position (this is called Hooke's Law. The constant k in the spring force is called the spring constant, and it has units dyne/cm.

Student build a differential equation for this phenomena and estimate parameters in the model from the dat they collect.