Pendulum Problems

Carlson, 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
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.