VelocityLab Investigation of Damped Harmonic Motion

This investigation shows how VelocityLab allows for a quick and easy demonstration of damped harmonic motion.  The photo below shows the experiment setup as performed by the author.  A jellied cranberry sauce can was selected as there is virtually no sloshing of the cranberry sauce as the can oscillates back-and-forth on a curved piece of laminate flooring.  The center of the flooring is clamped down to the table with an adjustable wrench.  The ends of the laminate flooring are raised a little with some small wood blocks.  The cranberry sauce can is shown at rest at the VelocityLab zero position.  PocketLab has been mounted to  one end of the can with some Velcro.
The video below shows a VelocityLab video combined with data for a typical run.  Note at the start of the video how the author carefully rolls the can to the top left side of the curved surface in a way that preserves the zero position and makes positions to the left of center negative while those to the right are positive.
The figure below shows a combined graph of position, speed, and acceleration vs. time. The graph was obtained by using Excel to massage the data in the pos_vel_acc.csv file produced by VelocityLab.  A number of questions about the video and graph are worth discussing with the students including:
1. What can be said about speed and acceleration when the cylinder is at maximum amplitude on either side of the curved surface?
2. What can be said about the speed and acceleration when the cylinder is rolling while at the center of the curved surface?
3. What happens to the magnitude of the maximum amplitude of position, velocity, and acceleration with each successive oscillation of the cylinder?
Graph of Position, Velocity, and Acceleration


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