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In this problem, you will use the program Logger Pro^{TM} to analyze motion. The instructions for using this program are given in the instructions document. We strongly recommend that you download and print this document for reference while doing this problem. You can find Logger Pro on any Mac in a campus computer lab, or you can download the 30-day trial version here.

The video that you can download here (right-click the link and save) shows a mass attached to a spring bouncing up and down. By analyzing the video, we want to figure out the equilibrium length of the hanging spring when there is no mass attached to it. The spring constant of the spring is 3.1 N/m and the mass hanging from the spring is 50 g.

A) Use Logger Pro to graph the spring length vs time. See the instruction document for details on how to do this. (Hint: carefully consider where you want to place to coordinate axes and what point on the spring or mass you want to track in order to come up with a graph of spring length vs time). A pre-setup Logger Pro file is available here.

B) Sketch the graphs of

- vertical velocity of the mass vs time
- vertical acceleration of the mass vs time

You can use Logger Pro to check your graphs, but you must say how you would use the position vs time graph and your knowledge about the motion of the spring and mass to make your graphs.

C) Using the graph of spring length vs time, find the equilibrium length of the spring with the mass attached (i.e. how long will the spring be when the mass attached and is not moving).

- If you want to know
the maximum value, minimum value, mean, or median of a section of a graph,
you can use the "statistics" feature in Logger Pro
- To do this, first highlight the section of the graph you want to know the statistics of.
- Go up to the "Analyze" menu and choose "Statistics." A box will appear with the statistics

D) What is the equilibrium length of the hanging spring when there is no mass attached?

Problem by Eric Kuo

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Page last modified February 9, 2009: O43