Pendulum Problems

Carlson, Robert Providence Catholic H.S.

Objectives 1. To review the terms pendulum, period, cycle, frequency, independent variable, dependent variable, damping, and displacement. 2. To review the graphs of the functions: f(x)=x0, f(x)=x1, f(x)=x2 3. To determine experimentally the relationship between the length (L) and the period (T) of a simple pendulum. 4. To derive the mathematical equation which represents the relationship. 5. To observe the graphical relationship between the period (T) and the displacement (d) of a simple pendulum. Apparatus weights (uniform mass)- one per student strings (increments of 10cm)- one per student overhead projector graph paper Apple computer/gameport/100k linear potentiometer (see Radio Shack) `Pendulum Plotter' disc meter stick stand/clamp Recommended Strategy 1. Construct a simple pendulum in front of class. Begin a dialogue concerning the motion of the pendulum. Use the words, period, frequency, cycle, independent and dependent variable, and control and try to elicit questions. After discussing the effects of modifying a pendulum, conclude that it is the length (under small displacement) that determines the period. 2. Provide each student with a pendulum. Have them determine the period of their pendulum. Discuss the significance of the number of cycles used to determine the period. Record data on the board. Also graph the period (dependent variable-T) versus the length (independent variable-L) using the vertical axis for (T) and the horizontal axis for (L). But instead of plotting points, tape each student's pendulum to the board. A curve is generated by the pendulum bobs but in this manner we see, maybe more convincingly, that it is the length of the pendulum that determines the period of the pendulum. 3. Distribute graph paper and, using the overhead projector, help the class to graph f(x)=x0, f(x)=x1, and f(x)=x2. Compare these
graphs with the graph generated in strategy 2 above. Lead class to
discover that the new function 'fits' between f(x)=x0 and f(x)=x1.
At this point, speculate that the new function could have a factor of
x1/2. Now try to get the kids to look back at the table to guess
what must be done to the 'L' values to get the 'T' values. With
'good' data you'll arrive at T= L1/2/5.

4. Fit the potentiometer to one end of a meter stick and affix this
apparatus to a ringstand. Using the gameport, wire the apparatus to
the computer. Boot the Pendulum Plotter program. Displace the meter
stick and observe the monitor for a graph which shows simple harmonic
motion. Allow time for experiments regarding the displacement of the
meterstick. What is being graphed now? Ask students to form conjectures
from their experiments.
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