```Pendulum ProblemsCarlson, Robert                     Providence Catholic H.S.                                    485-2136                           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
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 thesegraphs with the graph generated in strategy 2 above.  Lead class todiscover 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 ofx1/2.  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 themeterstick.  What is being graphed now? Ask students to form conjecturesfrom their experiments.```