B-1Harmonic Motion
1Setting up the pendulum
There are no questions to answer in Part 1.
2Testing the three variables
Table 1: Period, Amplitude, Mass, and Length Data
Number of Washers / Amplitude(degrees) / String Length
(cm) / Time from timer
(sec) / Period of pendulum
(sec)
3Analyzing the data
a. Of the three variables that you can change (length, mass, and angle), which one has the biggest effect on the pendulum, and why? In your answer you should consider how gravity accelerates objects of different mass.
b. Split up your data so that you can look at the effect of each of the three variables by making a separate graph showing how each one affects the period. To make a comparison easier, make sure all the graphs have the same scale on the y-axis (period). The graphs should be labeled one the x axis with A: String length, B: Mass (# of washers), C: Amplitude (degrees).
4Applying what you know
a. Using your data, design and construct a pendulum that you can use to accurately measure a time interval of 30 seconds. Test you pendulum clock against the timer set to stopwatch mode. Write down the variables that you chose. Also show any math that you did to come up with this pendulum.
b. Mark on your graph using a colored marker, the period you chose for your pendulum.
c. How many cycles did your pendulum complete in 30 seconds?
d. If mass does not affect the period, why is it important that the pendulum in a clock is heavy?
e. Calculate the percent error in your prediction of time from your pendulum clock. The percent error is 100 times the difference between your prediction and 30 seconds, divided by 30 seconds. Be sure to discuss this number in your conclusion.
5Damping and energy loss
1. To measure the energy-loss record the time it takes the pendulum amplitude to decrease from 30 degrees to 10 degrees.
2. Change the mass four times, keeping string length constant.
3. Change the string length four times, keeping the mass constant.
Table 2: Damping Data
Mass (washers) / String Length (cm) / Time to decay from 30 degrees to 10 degrees (sec)a. Plot two graphs that show how the damping time changes with mass and string length (time y-axis, mass or string length on x-axis).
b. Suppose you had to design a real pendulum clock that would keep swinging for many days. From the results of your experiment, how would you choose string length and mass? Explain how your choices are based on your observations.
Questions
1Describe a system (other than a bicycle) that has both linear and harmonic motion. Be sure to tell which part of the system is moving from one place to another and which part is moving harmonically.
2There are several examples of periodic motion associated with Earth. Name three, and give the period of each.
3A pendulum has a 35 cm string length. A student measures the period, then changes the string length to 60 cm. Will the new period (with the longer string) be longer, shorter, or the same as the first one? Why?
4A pendulum has a peg which causes the bob to swing in a tighter arc for half its swing. How does the period of this interrupted pendulum compare with the period of a pendulum with the same string length but an uninterrupted swing?