The Harmonic Motion of a Pendulum Name: ______

Copyright R. Mahoney 2010

> 101 students: Do only steps 1 through 3. <

The purpose of this lab is to verify that a pendulum moves in a simple harmonic fashion, that is, its equation of motion is based on Hooke's Law, and that its period is not amplitude dependent. Additionally we will show that a pendulum's period is not a function of the suspended mass, but only a function of the pendulum's length.

Answer all interspersed questions (Q) at the end of the lab.

Step 1. Set up your pendulum as shown in class. For a period of approximately 1.5 sec, the length of pendulum should be roughly 0.56 m.

Q1: Can you prove this?

Your first (spherically shaped) suspended mass (mass 1) should be the one that appears to be steel. Your second suspended mass (mass 2) should be the one that appears to be brass. Weigh mass 1, and attach it at a length of approximately 0.56 m. Watch the pendulum string's inflection or pivot point.

Length of pendulum: ______mMass 1: ______kg

Displace mass 1 about 10 degrees from vertical and allow it to swing freely for a few cycles. Remember that each cycle is "a swinging from one extreme to the other and back again". After the few cycles, measure the time for 20 cycles. In your counting of cycles, be sure to counr down to zero, then start your timer at zero, turning the timer off when you reach twenty.

Time for 20 cycles: ______secTime for one cycle (period): ______sec

This period is the experimental period for mass 1, for the length chosen above.

Using the formula given in class, calculate the theoretical period, and determine the percent error between the theoretical and experimental periods (theoretical as true).

Theoretical period: ______sec% Error: ______%

Step 2. Now repeat the above process, but for 40 cycles. Start with a larger initial angular amplitude of say 15 degrees. While you are counting your cycles and measuring their cumulative period, observe that over time the amplitudes of mass 1's oscillations decrease from the original 15 degrees to a smaller angle.

Time for 40 cycles: ______secExperimental period: ______sec

Now calculate the percent difference between the period determined in step 1 and the period determined in step 2. % Difference: ______%

(Q2: Did you see the period change because of a difference in initial amplitude?)

Step 3. Switch from mass 1 to mass 2. Make sure that the length of your pendulum stays about the same (it will probably change when the string is retied).

Length of pendulum: ______mMass 2: ______kg

Now repeat step 2.

Time for 40 cycles: ______secExperimental period: ______sec

Now calculate the percent difference between the experimental periods determined in step 2 and step 3. % Difference: ______%

Q3: Does the mass of the suspended mass in any way affect the period of a pendulum?

Step 4. Leaving mass 2 in place, decrease the length of your pendulum by about one half, and repeat step 3.

Time for 40 cycles: ______secExperimental period: ______sec

Theoretical period: ______sec

For this new pendulum length, determine the percent error between the theoretical and measured periods.

% Error: ______%

Q4: Did you expect the period to decrease by a factor of one half? Why is this not correct?

Step 5. State two non-trivial systematic errors for this experiment.

Step 6. Answer all interspersed questions here.