Amplitude And Length Of The Pendulum example essay topic

SPH 3 U: An Investigation of the Pendulum Corey McCormick Question: What are the relationships between the frequency of a simple pendulum and its amplitude, and length? Prior Knowledge: Variable SI Unit Definition Amplitude cm Distance from the equilibrium position to the maximum displacement. Frequency Hz The number of cycles per second. Label the amplitude and length of the pendulum below.

Materials: "h List the materials you have been given (and any other you decide to use) 1 A meter Stick 2 A 30 cm ruler 3 A piece of tape 4 100 cm+ of string 5 a washer 6 2 x desks 7 2 x chairs Hypotheses: "h Complete the hypotheses before the experiment. a) If the amplitude is increased, but the mass and length remain constant then the frequency will increase because the added amplitude allows the pendulum to gain more acceleration on the initial drop giving the pendulum a higher cycle per second rate (frequency). b) If the length is increased, but the mass and amplitude remain constant then the frequency will decrease because the longer the length, the less of an initial drop the bob has. A smaller drop forbids the bob to gain as much speed as it would have been able to obtain with a higher initial drop coming from a shorter length. Procedure: 1) The washer was tied to one end of the string. 2) The other end of the string was taped to the center of the meter stick which left exactly 90 cm of string in between the center of the washer and the meter stick. 3) The chairs were placed on top of the two desks, which had about 90 cm of space in between each other.

4) Each end of the meter stick was placed on top of the two chairs which gave the pendulum sufficient open space to swing back and forth from the center of the meter stick without hitting the ground or anything around it. 5) For part A) The 30 cm ruler was used to measure the various amplitudes: 6, 10, 14, 18, 22, and 26 cm that we were going to experiment with. Using the stopwatch, the time it took for our homemade pendulum to go through 20 cycles was recorded at each of the 6 amplitudes. This step was repeated to allow us to find an average time for each amplitude.

6) For part B) The 30 cm ruler was used to shorten the pendulum's length from 90 cm to 40 cm in 6 increments of 10 cm after each reading. Using the stopwatch, the time it took for the pendulum to go through 20 cycles, at an amplitude of 10 cm each time, (which was measured with the 30 cm ruler) was recorded. This step was repeated to allow us to find an average time for each length. Use graph paper to plot graphs of! SSFrequency vs. Amplitude!" and! SSFrequency vs. Length!" (see rules for graphing).

2. Answer the lab question by describing the two relationships. Use complete sentences. Change in Amplitude: During my research, I came to realize that my original hypothesis was wrong.

I was right when I said that with a larger amplitude there is a higher initial drop, giving the bob more time to accelerate, allowing the pendulum more speed. Although, I forgot that with a larger amplitude the pendulum has more distance to travel to make 1 cycle. I noticed that the extra speed gained by the pendulum from the larger amplitude somehow is proportional to the extra distance it has to travel to make 1 cycle, thus the frequency stayed constant with every change in amplitude. The frequency is the same at any given amplitude (as long as the length remains unchanged).

Change in length: While I investigated the pendulum, I came to realize that my original hypothesis was right. With a shorter length, the higher the initial drop is, allowing the pendulum more speed. Since I did not alter the amplitude at all during this part of the experiment, the pendulum's distance it had to travel to complete 1 cycle remained the same (10 cm) with each recording. Since a pendulum can obtain higher speeds with a shorter length, and altering the length does not affect the distance needed to travel to complete 1 cycle, I came to realize that the shorter the length is, the higher the frequency will be and vise versa. 3) Identify at least thee good sources of error in the investigation (i.e. three ways you could improve the accuracy of this lab). 1) Using a stopwatch was not an accurate method of timing the experiment.

When we hesitated even for 0.1 seconds when starting or stopping the timer, the readings of the experiment were affected. We should have used some sort of automatic machine to drop the washer, count its cycles, and time it. We would have had much more accurate readings than we did. 2) Using a washer was not the best object we could have used for a bob. When the pendulum was swinging, the washer would spin on its own. Every time the washer faced the direction it was going in, there was more wind resistance than when it was facing sideways and cutting through the air.

Every time the washer span around, there was that extra wind resistance which would slow the washer down just enough to minutely skew our readings. We should have used a rubber ball or anything else perfectly round so that the wind resistance would have been constant as the pendulum swung. 3) Being in an open room, there was constantly air moving around which would either push with or push against the bob depending on the direction it was swinging in. If our pendulum were placed in an airtight box, then there would have been no moving air to create wind resistance, giving us more accurate readings.