Pendulums

John J. Miller                 Maine East High School
                               6801 W. Dempster
                               Park Ridge IL 60048
                               (708)825-4484

Objectives:

The students will be able to determine what factors effect the period (time
to swing back and forth) of a Pendulum.  I use this for my sophomores in high 
school but don't let that fool you.  This can be used at any level where 
students can count to twenty and time something. 

Materials Needed:

pins
various lengths of string
washers (or any of various weights to hang)
clock with second hand (or anything to time with)
a long piece of cardboard or cork-board with a number-line marking off every 
   five seconds for up to one hundred seconds 

Strategy:

Tell the students to grab a length of string, tie a washer to one end and a 
loop at the other end of the string.  Next have the students time the period of 
twenty swings.  Have the students hang their washer at the spot on the number 
line that corresponds with the time they have found.  There should be a pattern 
that looks something like this: 
             
      | |  |  | | | ||
      O O  |  | | | ||
           |  | | | ||
           O  | | | ||
              | | | ||
              O | | ||
                | | ||
                | | ||
                O | ||
                  O ||
                    ||
                    ||
                    O|
                     O

Ask the students what factors would affect the period of the swing.  With 
encouragement, I bet they'll come up with length of string, mass, amplitude (how 
wide an arc), whether the hand moves or not, and possiblely some others.  Break 
the students up into groups and have each group investigate these factors by 
keeping all factors constant except the one they are investigating.  Have each 
group report back to the class with their findings. 


Performance Assessment:

The verbal report to the group may be graded.  I believe the ideas of particular
interest include whether or not the group controlled the variables, did they 
actually make accurate measurements and present the data (not just guess or 
approximate) and then the actual presentation. 

Conclusions:

1. Mass of the hanging objects does NOT make a difference.
2. The amplitude does NOT make a difference (for amplitudes less than 40 
   degrees).
3. Length of the string DOES make a difference.  There is a formula if you
   wish to check it.  (Period=2(3.14)Square-root(Length/gravity) or 
    T=2pi*sqrt(l/g))
4. Small hand movements do not make a difference extreme hand movements will.

Reference:

     Me! Call me anytime for help.