Brewer Period of Pendulum Lab

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Dec 6, 2023

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NAME: Period of a Pendulum BACKGROUND A pendulum is a bob hanging from a string that is made to swing back and forth. In the absence of friction and air resistance , the bob will repeat its motion indefinitely. The motion is a repetition of a “ cycle .” The time (in seconds) taken to complete a cycle is called the “ period ” of the pendulum. In this experiment we will study the effect of different variables on the period of the frictionless swinging bob; that is we will try to see how we can change the period of oscillation. AIM To identify factors that affect the period of a pendulum PROCEDURE Go to https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html Click on INTRO. Set: length = 0.7m mass = 0.2 kg gravity = Earth Friction = None 1

NAME: Stopwatch = ON Speed = Normal 1. Displace the mass to the side by about 30 degrees and let the mass swing. The mass moves from one extreme point, through the center, to the extreme point on the other side and then back to the starting point. Watch the repetitive pattern and figure out what you would define as one cycle . (There is more than one configuration that can be considered a cycle.) Q1. What will you consider to be a cycle – describe where the mass starts and where the motion finishes: A cycle is when the mass moves from starting point to opposite, most extreme point, and returns to its starting point. 2. Click on “ Period Trace” to see a path that is one complete cycle. (There are more convenient paths that make up a cycle.) Q2. As you watch the pendulum oscillate, consider what factors might affect the oscillations. List three possible factors: Angle of origin, gravity, and length of rope. 3. Set the mass into oscillations and practice finding the time taken for 3 oscillations using the stopwatch. 4. Once you are comfortable measuring the time for oscillations, start finding the time taken for 5oscillations by changing the angle through which it is displaced. Do this twice for each angle of displacement and then take the average. The period is the time taken for once cycle , so divide the average value by 10 to get the period in the last data column. DO NOT CHANGE ANY OTHER PARAMETERS. Pendulum length = 0.7m. Note: t average = (t 1 + t 2 ) / 2 2

NAME: Table 1. Period measured by varying angle Angle Time for 5 oscillations Period T (1/s) (degrees) t 1 (s) t 2 (s) t average (s) T = t average /5 30 8.53 8.51 8.52 1.704 25 8.44 8.44 8.44 1.688 20 8.48 8.50 8.49 1.698 15 8.39 8.40 8.395 1.679 5 8.34 8.33 8.335 1.667 When you vary the angle through which the pendulum oscillates you are changing the amplitude of oscillation. Q3: Based on the data in table 1, does period depend on the amplitude of oscillation? Explain. Yes, but not significantly. As the degrees decreased the periods of oscillation only decreased by hundreds of seconds. 5. Now vary the length of the pendulum and measure the period like you did before. This time the angle of displacement will be 30 degrees for all trials. Table 2. Period measured by varying length Length Time for 5 oscillations Period T (1/s) m t 1 (s) t 2 (s) t average (s) T = t average /5 1.00 10.17 10.17 10.17 2.034 0.93 9.86 9.88 9.87 1.974 0.87 9.64 9.63 9.635 1.927 0.80 9.06 9.06 9.06 1.812 0.70 8.55 8.54 8.545 1.709 0.63 8.12 8.12 8.12 1.624 0.57 7.7 7.71 7.705 1.541 0.50 7.18 7.20 7.19 1.438 0.1 3.28 3.28 3.28 0.656 3

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NAME: Q 4: Does changing the length of the pendulum affect the period of oscillation? Explain. Yes it does. Changing the length of the pendulum changes the distance it has to travel to complete a cycle, thus changing the time. 6. Next vary the mass of the bob and find the period of oscillation. Keep the angle at 30 degrees and the length at 0.70m. Table 3. Period measured by varying mass Mass Time for 5 oscillations Period T (1/s) (kg) t 1 (s) t 2 (s) t average (s) T = t average /5 0.2 8.53 8.53 8.53 1.706 0.5 8.53 8.52 8.525 1.705 0.75 8.53 8.53 8.53 1.706 0.9 8.52 8.53 8.525 1.705 1.1 8.53 8.82 8.525 1.705 Q 5: Does changing the mass of the pendulum affect the period of oscillation? Explain. No, since the pendulum is free falling, gravity is what determines its speed, not its mass. Q 6. Summarize your results from table 1, 2 and 3. What factors affect the period of the pendulum and what factors do not affect the period? 4

NAME: Table one showed that angle has minimal affect on time of period. Table 2 showed that variation in length of pendulum has the greatest impact on time of period. And Table 3 showed that mass has no affect on time of period. Length has the most significant affect, and angle has a slight affect. Mass does not affect the period. Q 7. Can we find any other factor that might affect the period? Look at the possible variables in the program and see if you can find another one to vary. Does this affect the period of oscillation? Explain clearly or show your data below to support your answer. Yes, both gravity and friction affect the period of oscillation. Changes in gravity result in the pendulum moving at different speeds, and the addition of friction will eventually cause the pendulum to stop. 7. Additional analysis: In Q 6 you have found out which variables affect the time period. Graphing is another way to see the relationship between variables. It can also show if the two variables vary linearly, inversely, quadratically, etc. Using the data from tables 1,2 and 3, plot graphs of the following and figure out the relationship between the variables. Next to each of these, write down whether the relationship is linear, inverse, independent, quadratic or other. (a) Period T vs mass ___independent ______ (b) Period T vs length of pendulum _____Quadratic_______ (c) Period T 2 vs (length of pendulum) ________Linear____ (d) Period T vs amplitude/angle _______inedependent______ You can plot these on graph paper or use Excel, Demos online or https://phet.colorado.edu/sims/html/curve-fitting/latest/curve-fitting_en.html 8. If you have studied the oscillations of a simple pendulum you know that the period T is related to the length  and free-fall acceleration g by Do any of your graphs support this relationship? Explain. Yes, graph 2 shows this by there being a linear relationship between changes in length and changes in period. 5

NAME: 9. From that graph determine the value for g . Slope of graph = __1.5101_____ 6

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