Return to Physics IndexPeriodic Motion - The Pendulum

Deborah Lojkutz Joliet West High School

401 N. Larkin Ave.

Joliet IL 60435

(815) 727-6950Objectives:

To introduce the concept of periodic motion and relate it to the movement of a

pendulum. To discover that the period of a pendulum is dependent on the length

of the pendulum and independent of the bob and the amplitude.

Materials needed:

Each group needs a stop watch and pendulum with a different bob.

Materials for pendulum -

string

bob - infant stacking rings provide colorful bobs of different sizes and mass

right angle clamp

ringstand

rod

For class graphs - two pieces of end roll paper approximately 21/2 meters long,

a meter stick, markers and masking tapeStrategy:

Begin the class period with a discussion of what the students think periodic

motion is. After a few minutes, bring out a pendulum from behind the lab table

and use it as an example of periodic motion. Point out its various parts - bob,

length, pivot point. Demonstrate what is meant by period and amplitude. Spend

a few minutes discussing the accuracy of measuring a single period. The

students should realize that timing how long it takes for ten cycles and

dividing by 10 will lessen the effects of reaction time and result in a more

accurate measurement of the period.

Break up the class into groups. Each group is given a pendulum with a different

bob but all pendulums are 1 meter in length. (A different option would be to

have the students construct their own pendulums 1 meter in length. If doing so,

make sure to discuss that the length of the pendulum is measured from the pivot

point to the center of gravity of the pendulum bob.) Each group is to find the

period of their pendulum by timing it for 10 cycles and using an amplitude of

10 cm. After doing so, they are to experiment with other amplitudes (5 cm,

15 cm, 20 cm, etc.) to determine if the amplitude effects the period. All

groups record their data in the class data table on the board under the

following headings: Color of bob, Time for 10 cycles, Period, Effect of changing

the amplitude.

When all groups have recorded their data, call the class together for a

discussion of the results. It should be apparent that the shape and mass of the

bob and the amplitude have no effect on the period. Small differences can be

explained by experimental error. If the students are not sure that the rings

are actually different masses, bring out a scale and prove it. If you are using

infant stacking rings, there will be about a 50% difference between the largest

and smallest ring's mass.

Each group is given a different length of string to create a new pendulum.

Lengths should vary from 25 cm to 2 m. As before the groups will find the

period of their pendulum. This time they will graph their results on a length

versus period graph.

While the students are finding the period of their pendulums, hang a piece of

end roll paper about 21/2 meters long on a wall and label the axes. The vertical

axis is marked off to the actual length of the pendulum. The horizontal axis is

the period marked in a convenient scale.

When the students have found the period of their pendulum they should remove it

from its support bar and hang it on the graph at its corresponding period.

Remind the students that the actual length of the pendulum is measured from the

pivot to the center of gravity of the bob. When using rings for bobs, the

center of gravity is at the center of the ring, therefore it is important that

the centers of the rings be lined up on the horizontal axis. By using this self

graphing technique, it is not necessary for the students to measure the

pendulum's length and the effect of the length of the pendulum on the period is

shown quite dramatically.

Once all groups have added their pendulums to the graph discuss the results.

The graph should look like a y-parabola. If it is not obvious that it is a

parabola remember that the origin is a point on the graph - zero length will

have zero period. With a marker sketch the curve on the graph. Discuss with

the students the shape of the graph and what it represents mathematically.

Hopefully they will come up with the idea that there is a direct relationship

between the length and the square of the period. (This depends on their level

of math ability.) If this relationship is not obvious, lead the students by a

discussion of what needs to be done to straighten out the graph. This approach

usually gets to the idea of squaring the period. The students should now verify

these predictions by squaring their period and regraphing on the second end roll

graph. The students should transfer their pendulums from the first to the

second graph. The resulting graph should be a straight line through the origin.

At this point the class can discuss the results that the square of the period is

directly proportional to the length of the pendulum. This would be a good point

to start a discussion of the equation and theory of a pendulum.Conclusion:

This activity will take more than the usual lab period. A good breaking point

would be after finding the effect of the bob and the amplitude. This activity

can be used with elementary students up to the first graph.Evaluation:

The student's understanding of this material can be evaluated by having them

use the graph to predict what the period of a pendulum will be for a specific

length. They can then experimentally verify their prediction.