Lab 4 (online): Pendulum and Simple Harmonic Motion (Friday, 11-4-2022) (due 11:59 pm, Wednesday, Nov 9, 2022. A formal report is required) https://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html mg F =-mg sin 0 = -mg0 =-mg , X = -X L Compare to the SHM, k - mg k 8 or T = = 21 m mg sin omg cos 0 mg 417 2 T2 g Procedures 1. Prove the independence of Tor @ on mass (with fixed L and small angle (less than 15 deg) but 3 different masses) 2. Prove the independence of T or @ on initial angle or amplitude (with fixed L and small angle (less than 15 deg) 3. Find the gravitational acceleration on the earth surface, g (make a table) (a) fix a mass (e.g. 0.5 kg) (b) record for each / (/ =0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 m) (c) calculate 72 (d) plot 72 (y-axis) against / (x-axis) (e) find the slope of the plotted straight line (f) calculate g, g = 4n/slope (why?) 72 Table 1 Period measurement for different string length I(m) T(s) I' (s2 ) 0.4 0.5 0.6 0.7 0.8 0.9 Slope = (s'/m) g= (m/s2) error% =4. 6. Find the gravitational acceleration on the moon, gmm {just use one measurement, multiple measurements in step 3 will reduce the experimental error}. Find gm... 1: (m) T = (3) 3mm = (mils?) Measure T for three angles {fix mass and L and measure T with 3 initial angles [5, 10 and 30 deg}. Are the values of T{5} and T {10} very close? What about T(30}? Explain if vou find the value that differs from T{5} or T{1D}. Table 2 Period measurement for different angles. | Initial Angle {deg} | Period {5} S | | | 10 | | 30 | Apply different amount of friction and observe the decav of the oscillations (no data collection). Exercise (optional, 15 bonus points] The general expression of the oscillations can be written as x = Acos(mt+ a). If we initially release the mass with (i; = \"/13 and gave a push with v0 = 1/18 m/s at t = O, [1} find the amplitudeA and initial phase a (2) plot the oscillation against time {2 "' 3 complete cycles}. This will help you to better understand the initial conditions and all the parameters. (i. = 1 m, m = 0.5 kg, Blet, and assume tan(x} = x, 337:2, n1 + llnzznz} Tips for Writing Lab Reports A full lab report should contain an abstract, an introduction/description of methods section, a sample calculation, a data section, answers to any required questions 3: exercises, and a conclusion. This document explains each of these sections and how to make sure you get the best grade possible. Abstract The abstract is a brief overview of your experiment. It should concisely do the following three things: 1. Fully state the purpose of the experiment and how it relates to the lecture. 2. Describe the procedure of the experiment. This should only take one or two sentences. 3. Present experimental results. (Example: "We found that value X agreed with what was expected in theory with a percent difference of 2%.) Introduction/ Description of Methods This is where you will fully describe the procedure of the experiment. What equipment you used, and what you did with it. Your description of methods should: 1. Name all equipment and instruments used to complete the experiment. 2. Describe all steps taken using the equipment to complete the experiment. Sample Calculation A sample calculation is as the name suggests - an example of the calculations you performed during the experiment. The sample calculation should: 1. Show a relevant equation used to calculate your data points. 2. Apply the equation using data from your experiment. 3. Give a numerical answer with correct units. Experimental Data and Graph(s) This section should contain all data from your experiment. This includes data tables and any graphs that are required. Your graphs should always have a title and axis labels with units. Please be sure to attach the original data (the data you record in your lab pages). You may scan your lab sheets or take a picture of them, and you may screenshot your graphs or save them as an image. You may share your data with your lab partners, but you must write your lab reports separately. Questions 8: Exercises You must include answers to any required questions and exercises that go along with the lab, and show any steps you took to get to your