THIS IS ALL THE Information I HAVE. The first page is the lab, The rest is about how to do the lab. can you please provide a screenshot from the simulation and the Excel graph?

DETAILED INSTRUCTIONS FOR LAB ACTIVITY COMPLETION: This is your lab activity for the course chapter thirteen (13). Therefore, the rst step is to visit the following webpage: https :f'fphetcolorado.edw'enfsimulationfpendulum-lab The purpose of this webpage is to provide you with the simulation to complete this lab activity. This lab activity requires you to produce a lab report. OBJECTIVES: Objectives At the end of this lab activity. the student Solve problems involving sound and should be able to -) sound waves. At the end of this lab activity, the student \"\"59 9343311111911 5 311' \"'1'1 e 53 ' 5 3 013' should be able to -) laboratory reports. INSTRUCTIONS FOR COMPLETING THE LAB ACTIVITY: 1. Click on \"Run Now\" within the simulation. The link to the simulation was provided in the \"DETAILED DIRECTIONS FOR LAB ACTIVITY COMPLETION.\" 2. Run the simulation. 3. Use the simulation to develop the laboratory report. 4. Ensure that you have completed the lab report. DIRECTIONS TO DEVELOP LAB REPORT: 1. For this section, you must write a laboratory report to determine the relationship between the length of a pendulum and its period. Use the simulation to conduct your experiment and gather data for this section. Under the heading, \"Supporting Activities,\" some possible activities are given (These activities are to give you an understanding of the experiments you can use for your lab report). 2. Follow the general outline of a lab report as provided in the link below: http:x'fwww.utm.edur'stai'cerkalr'reporthtml 3. Remember to show your calculations. These laboratory reports will prepare you to do well in future lab activities and in the project. Supporting Activities (Provided only to support the develo ment of your lab report Do not submit the activities given here wit the lab report n this section, you only have to produce the lab report covering all the headings of a lab report with data and calculations): a) What is the equation for the period of a pendulum? b) Why is the period of a pendulum not dependent on its weight? c) Is the relationship between the length of a pendulum and its period is valid at all times? * You only need to submit a comprehensive lab report. Lab 13: Simple Pendulum Objectives . Investigate the oscillatory motion of a simple pendulum - Determine how the period of a pendulum depends upon amplitude, mass, length. 111eory In this lab, you will do an experiment that was performed by Galileo around 1602. A simple pendulum can be constructed easily by hanging a mass on the end of a string and letting it sway back and forth in a gentle arc. (We will be using the metsimulation). Open the simulation by going to hps:ffphetcolorado.edufenfsimulationfpendulum-lab Just use the rst choice on the left that says Intro. In general, the oscillatory motion of a pendulum involves a rather complicated mathematical formula. However, there is a "simple" approximation that works well when the angle is small. For this lab, you'll be using angles that are 30 or less. Don't use an angle greater than 30 degrees. There are several terms involved in oscillatory motion that need to be explained: 1. Oscillation period T: the time it takes to swing forth and back to its original position, thus completing one full cycle. This is the dependent variable because it will be the variable that may or may not depend on the change in another variable. This goes on the y axis of your graph. Remember that just as the previous labs I will only count graphs that are created using Exoel that show the equation of best t and are labelled correctly. 2. Mass m: the mass of the attached object. This will be the independent variable in your rst experiment. 3. Initial angle 9: the angular displacement away from equilibrium when you release the pendulum. This will be the independent variable in your second experiment. 4. Length L: the length measured from the pivot to the center of mass of the object attached. This will be the independent variable in your third experiment. Procedure In this particular lab, your goal is to gure out the relationship between the period and the mass, then the period of the pendulum and the angle, then the period of the pendulum and the length of the pendulum. It is up to you to decide the specic details for this experiment. (g9: number of data points to take) However, reasonable methods, and a good number of data points are still expected. Be sure to explain your methods and present your data in a clear fashion. This means to produce data tables showing all data and graphs should be presented using Excel and the equation of best t and labels should be included. Experiment #1 Determine whether the oscillation period T of a pendulum depends upon mass m on the end of a string. a. Base on your intuition, what would happen to the period T if you increase the mass m? The result of this experiment should be a graph of period vs mass. b. Measure oscillation period T with different masses, using any method available. Keep the initial angle and string length constant. c. In Excel, graph period T as a function of mass m. T goes on the y axis and m goes on the x axis. Make sure that you can see the zero, zero on both axis of the graph. If you don't do this the graph will seem like there is a relationship when there is really not one. Look at the Wyou will see that the 0,0 data can't be seen. If you look closely at the equation for this graph, he slope is pretty much equal to ze_:o but it looks like there is a relationsh . Email me if you can't do this. Oscillation Period vs Angle of Motion y = 0.0013): + 1.66695 1.?1 1.705 t\" --.i 1.695 1.69 1.685 1.68 1.6?5 0 5 10 15 20 25 30 35 Oscillation Period {5] Angle of Motion Here is the same graph but I went into the y axis and changed the minimum value to zero and the maximum value to 2. You can now see that the period does NOT change when the angle is changed. Notice that the equation for the graph has not changed because it is the exact same data. Oscillation Period vs Angle of Motion y = 0.0013): + 1.66695 N ....-. l" U'l Oscillation Period {5] 8 H o 5 10 15 20 25 30 35 Angle of Motion d. What do you conclude from the graph? Does it match your expectation? (Discuss!) Experiment #2 Determine whether the oscillation period T of a pendulum depends upon the angle 0 of its motion. e. Base on your intuition, what would happen to the period T if you increase the initial angle 0? f. Measure the oscillation period T with different angles (30 or less), using any method available. Keep the mass and string length constant. g. Graph period T as a function of angle 0. T goes on the y axis and angle goes on the x axis. Make sure that you can see the zero, zero on both axis of the graph. Email me if you can't do this. h. What do you conclude from the graph? Does it match your expectation? (Discuss!) Experiment #3 Determine whether the oscillation period T of a pendulum depends upon the length L. i. Base on your intuition, what would happen to the period T if you increase the length L? j. Measure the oscillation period T with different lengths L. You will need to use many values for length to get this graph correct. Use some lengths that are as small as the simulation will allow and some that are as large as it will allow. It may take as many as 10 trials for you to get this curve to have the right shape. Keep the mass and the initial angle constant. k. Graph period T as a function of length L. T goes on the y axis and length goes on the x axis. Make sure that you can see the zero, zero on both axis of the graph. Email me if you can't do this. This part is important! Do not assume that this is a straight line. I'll go ahead and tell you that there is a relationship here but NOT a linear relationship. It is a square root curve. Google that and research that relationship if you need to So, if you create a graph, don't bother applying a linear fit in Excel because it will be a square root curve not a linear curve. I. What do you conclude? Does it match your expectation? (Discuss!)Galileo discovered that the period T of a simple pendulum is approximated by the formula below. L T = 211' . Eq. 1 .9 So, this is where you will have to do some algebra. If you rearrange the equation above so that it is: T = (jEJx/E Therefore, you now have to take the same data that you collected, when you graphed T vs. Length, but now take the square root of the length, and graph T vs. JE, according to Galileo's equation your slope should b_e. Y=mx ,/l\\. T = (jgwi Is this result consistent with what you discovered in 1, 2, and 3? Discuss if this equation is valid based on what you see in all the graphs. It will be appropriate to graph T vex/E graph and nd the slope of the trendline for your discussion. Now if you slope is equal to the below expression, then you will take your slope and calculate an experimental value for g. Compare that experimental value to the accepted value of g which is 9.8m/sA2 and calculate the percent error. Comment on that percent error in your conclusion