A simple pendulum consists of a mass called the pendulum bob suspended from a support by a thread. A complete vibration of a pendulum consists of one swing over and one swing back. The time for a complete vibration is called the period (T) of a pendulum. This is usually measured in seconds.
When a pendulum swings through a small arc, its bob is undergoing sample harmonic motion. The force causing the bob to swing along its arc is greatest when its speed is least. The force is least when the speed of the bob is the greatest.
Objectives:
During this investigation you will:
(a) Test the effect of the certain variables on the period of a pendulum.
(b) Learn to use a graphical method as a means of determining mathematical relationships that describe physical phenomenon.
Procedure:
1. Suspend the 50-gram and the 100-gram pendulum side by side. Make each pendulum the same length (50 cm as measured from the point of support to the center of each bob).
2. Using a ruler, pull the bobs aside together to the same height (about simultaneously by quickly dropping the ruler. Observe the two bobs of different mass as they swing through their arcs. Record you observations in the Data and Calculations section.
3. Start the bobs swinging simultaneously again, but this time release each from a different height. Observe the bobs to see if they both arrive at the bottom of their swings together. Do they each swing through their different arcs in the same or different times? Observe over several swings. Record you observations in the Data and Calculations section.
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4. Remove one of the pendulum. Vary the length of the remaining pendulum by grasping the thread at different distances from the bob and allowing the bob to swing through several vibrations. Record your observations in the Data and Calculations section.
5. To be more quantitative, use your stopwatch to measure the time required for pendulum of different lengths to swing through 40 complete vibrations. Begin with the 50-cm pendulum. Record this time in Table 13-1.
6. Repeat Steps 5 and 6 for each of the pendulum lengths listed in the table. Enter your data in 13-1.
Observations:
We observed that as the string started to decrease in size, the pendulum would complete vibrations faster, and this shows that the longer the string, the more time it takes for the pendulum to complete the turn.
Heavy
The table above shows the results for the experiment, with heavy weight, when we used the weight as the pendulum bob, and recorded time for 40 vibrations with certain string length.
Light
The table above shows the same experiment done, but now with the weight, that is about 100g compared to 550g, and the results are recorded.
Calculations
The table above shows the calculations made figuring out the period by dividing the total time required by the number of vibrations, the second column is the s squared.
Calculations
The above table shows the results put into equation for finding the period, dividing the time by the number of vibrations.
Conclusion:
In performing this lab, we noticed that the string length made the difference in the number of vibrations in 40 seconds. We can see from the tables that as the length of string was decreased by increments of 10, the number of vibrations started to take less and less time. This show that the long string takes its time and goes slow and compared to the 10 cm string, the long string definitely takes long, and the short string goes with more speed. The results in the tables are with some fault, due to human error. We were not really accurate as to collect time for 40 vibrations, but we still notice changes and see the results have a point. By comparing the results from both tables, one for small weight and one for large, we notice that although the results are a little bit different, but they are still very close and this makes it safe to conclude that the weight did not affect the speed of the vibration, that mainly depended on the height.
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