Question for consideration:What factors influence the period of oscillations for a swinging pendulum that has mass located only at the plumb bob end? (The mass of the string is considered to be negligibly small.)

Factors to consider:
The amplitude (angle of release from vertical) The hanging mass (or the “plumb bob” mass)
The length of the pendulum Gravity (does gravity affect pendulum motion?)

Go to the website http://phet.colorado.edu/ and click on the blue “Play with Simulations” button. Select “Physics” from the list of simulations on the left side of the page and scroll way down to select “Pendulum Lab.” Click the play button (sideways triangle in a circle) in the center of the Pendulum Lab graphic on the page.

Familiarize yourself with the layout of the new page and the operation of the simulation. You will be varying the length of the pendulum and the mass attached to the string using the slide bars at the top of the green box on the right. Do not display a 2nd pendulum (for this lab), ensure that the friction bar is set to “none”, that “real time” is selected (not ¼ time or 1/16 time), and that “Earth” is selected for a planet. Check the photogate timer box at the bottom of the green box. Click and drag the bob to either side to the desired angle; click “pause/play” to set the pendulum in motion or to stop the motion. Click the green “Start” button on the photogate timer to record the time for one complete cycle of oscillation of the pendulum. When finished taking measurements for a given set of conditions, click the “pause/play” button to stop the pendulum motion and click the red “Reset” button at the bottom of the green box.

Repeat the procedure given in the previous paragraph for each set of conditions given in the table below, recording your findings as you proceed.

Select Gravity for Earth (green box)
Length Amplitude Mass Record Period
from Timer
1 meter 15° 1.00 kg
1 meter 15° 2.00 kg
1 meter 30° 1.00 kg
1 meter 30° 2.00 kg

2 meter 15° 1.00 kg
2 meter 15° 2.00 kg
2 meter 30° 1.00 kg
2 meter 30° 2.00 kg

Select one set of conditions from the table above and click the “velocity” box so that you can observe the velocity of the bob as it moves through its various angular displacements. Reconcile in your mind the displacements and velocities displayed in the simulations as compared to discussions in class, graphs in the lecture PowerPoints, and in the material in the textbook. That is, where is the velocity at its minimum and maximum – when the pendulum is at the greatest amplitude, or when the pendulum is at the center?

Select one set of conditions from the table above, deselect the “velocity” box, and then click the “acceleration” box so that you can observe the acceleration of the bob as it moves through its various angular displacements. Reconcile in your mind the displacements and accelerations displayed in the simulations as compared to discussions in class, graphs in the lecture PowerPoints, and in the material in the textbook. That is, where is the acceleration at its minimum and maximum – when the pendulum is at the greatest amplitude, or when the pendulum is at the center?

Click the radio button for the Moon (not Earth) and fill out the following table for a pendulum motion.

Select Gravity for Moon (green box)
Length Amplitude Mass Record Period
from Timer
1 meter 15° 1.00 kg
1 meter 15° 2.00 kg
1 meter 30° 1.00 kg
1 meter 30° 2.00 kg

2 meter 15° 1.00 kg
2 meter 15° 2.00 kg
2 meter 30° 1.00 kg
2 meter 30° 2.00 kg
Keep the Length, Amplitude, and Mass at the last values from the table above. Set the pendulum in motion, and, while it is moving, click the “g = 0” button. In other words, turn off gravity after the pendulum is in motion. Fill out the table below, or otherwise describe what you observe on the screen.

Zero Gravity (green box)
Length Amplitude Mass Record Period
from Timer
2 meter 30° 2.00 kg

Pause the simulation and Reset the position. Keeping the Length, Amplitude, and Mass the same, and the gravity at Zero, move the pendulum to the side and start the simulation. Describe what you observe.

Answer the following questions. Attach extra pages or write on the back of the paper, as needed, to complete this lab.

1. Keeping everything else the same, how does the period of oscillation change when the mass of the pendulum doubles?
a.) doubles b.) quadruples c.) decreases by a factor of 2 d.) decreases by a factor of 4
e.) increases by a factor of v2 f.) decreases by a factor of v2 g.) does not change
2. Keeping everything else the same, how does the period of oscillation change when the amplitude of the pendulum doubles?
a.) doubles b.) quadruples c.) decreases by a factor of 2 d.) decreases by a factor of 4
e.) increases by a factor of v2 f.) decreases by a factor of v2 g.) does not change
3. Keeping everything else the same, how does the period of oscillation change when the length of the pendulum doubles?
a.) doubles b.) quadruples c.) decreases by a factor of 2 d.) decreases by a factor of 4
e.) increases by a factor of v2 f.) decreases by a factor of v2 g.) does not change
4. For the Earth pendulum, at what swinging position is the velocity greatest? Where is the acceleration greatest? Describe how the formulas from class support your answer.

5. Explain in words why the results are different on the Moon than they are on Earth. Write out formulas from the text that support your observations and explanation.
6. Explain what happened when the pendulum was in motion, and gravity was turned off ( g = 0 ). Why did it behave the way that it did? Is there a Law of Physics that explains this?
7. Explain why the pendulum behaved in the way that it did when the bob was moved from the center line and released in zero gravity. Be specific.