Slinky Toys and Harmonic Motion                                            Barb Lamb

Adapted from an activity by Greg Hill

 

 

 

James Industries, Inc. of Hollidaysburg, PA manufactures the favorite toy of many of us as kids, the Slinky.  They are concerned about the quality of some of their Slinkys and wish for us to test them.   We are to test the “bouncing quality” of some Slinkys.  The company is hoping that the toy “bounces” up and down fairly quickly and consistently.  They do not want any to be sold that are “too loose”;  i.e., they take too much time to complete one “bounce” up an down.

 

 

 

You will need:             one Slinky, one motion detector (CBR), your TI-83, a writing utensil, some tape, small pieces of cardboard or paper, and scissors

 

 

Procedure:

 

  1. Cut out a circle of cardboard or paper to fit one end of the Slinky (we want to cover one end up).  Tape it onto that one end.

 

  1. Set up the CBR on the floor and practice “bouncing” the Slinky directly over the motion detector.  Make sure that the spring will be at least ˝ meter away from the motion detector when it oscillates.  Be sure that the covered end is toward the floor.

 

  1. Turn your calculator on, choose Ranger and in the setup, choose to collect distance in meters for 2 seconds.

 

  1. Sketch a prediction of what you think the graph will look like.  Sketch it below with labeled scales.

 

 

 

  1. Get the Slinky to oscillate smoothly BEFORE collecting your data.  Remember to try NOT to force the Slinky to go up and down, like you would with a yo-yo.  Once you get a consistent motion, collect your data using the motion detector.

 

  1. If your data does not look reasonable, or if you think that your Slinky did not remain directly over the motion detector, choose to re-do the data collection.

 

  1. Once you get a reasonable set of data points, quit properly from the program.  The program will tell you what data is in which lists.  Make a note of those lists.

 

  1. Use  ZoomPlot to graph this data.  Sketch what appears on your screen here:

How close is this to your predicted graph in #4?

 

 

You need to write an equation for your graph in  y = A cos [b(x-c)] + d form.

You may use paper and pencil or some of the features on your graphing calculator, but NOT a regression.   Show any work below.

 

 

Y = ________________________________________

 

 

 

 

 

List your values for:

 

Amplitude = ______________________

Period = ________________________

Phase shift = ______________________

Vertical shift = ___________________

 

 

Based on some of these values, does your Slinky “bounce” fairly quickly and consistently, or is it “too slow” and should it be sent back to the company?

 

 

P.S.  Why did we cover one end of the Slinky up early in this procedure?

 

Teacher Notes:

 

1.        Bouncing the Slinky directly over the motion detector is important;  be sure the students practice this before collecting data.

2.        Equations will vary somewhat depending on data collected.