Physics 4C Simple Harmonic Motion PhET Lab Scott Hildreth Chabot College Goal: Explore principles of Simple Harmonic Motion through both hanging masses and pendula. Then, verify your understanding of how oscillation frequency depends upon mass and spring constants with a brief validation of the theory. Materials needed: Computer, Spring, Table Clamp, Rods, Clamps, Timer (phones are fine). Lab Report Expectations: This is a worksheet lab, and a formal lab report is NOT required by each group. You will need to turn in one clean completed copy of this worksheet for each team, along with screen-shots of the graphs you create in Part 1, and with each participating member clearly listed below. In addition to the worksheet and graphs, each of you must write and submit your own *abstract* summarizing the results obtained for Part 3: Testing Simple Harmonic Motion with a Spring. Please read the lab report guidelines for what should be included in a comprehensive, professional abstract. The abstract is due in two weeks, on or before class starts on 9/8. Lab Team Members: Part 1: Access the Simple Pendulum PhET Simulation online at https://phet.colorado.edu/en/simulation/legacy/pendulum-lab and click on: PREDICTIONS 1. How does the period of the pendulum depend on the amplitude of the swing? 2. How does the period depend on the length of the pendulum? 3. How does the period depend on the mass of the pendulum bob? 4. How does the gravitational acceleration affect the motion of the pendulum?
PROCEDURE A. Period and Amplitude 1. Click the lower right button to activate the photogate timer. 2. Set the mass to 1.00 kg, length to 1.00 m and amplitude to 1. 3. Start the photogate timer. This will automatically stop when it has recorded the time for one complete swing (one period). 4. Record in a spreadsheet (Excel or Open Office) the Amplitude and Period in two consecutive columns. Label each column with the corresponding units. 5. Continue to take readings for amplitudes 2, 3. 4 and 5. 6. Highlight the columns with numerical values on your spreadsheet and insert a scatter plot. Choose a layout that will allow you to add graph title and axes title with complete unit. 7. Take a screen shot (use the Snipping Tool available in the command menu) of the graph. You can save, copy, and paste the image into a file that will be submitted along with the worksheet for your team report. Reset before continuing to part B. B. Period and Length 1. Keep the amplitude at 5, the mass at 1.00 kg and gather data for different lengths as follows: 0.50 m, 0.60 m, 0.70 m and 0.80 m. 2. Enter your data on the spreadsheet software, labeling the axes appropriately. 3. Take another screen shot of the graph, save it, and copy it to your lab report file. Reset before continuing to part C. C. Period and Mass 1. Keep the amplitude at 5, the length at 1.00 m and gather data for different mass values as follows: 0.50 kg, 1.00 kg, 1.50 kg and 2.00 kg. 2. Enter your data on the spreadsheet software, labeling the axes appropriately. 3. Take another screen shot of the graph, save it, and copy it to your lab report file.
QUALITATIVE ANALYSIS 1. Analyze each graph and determine the relationship between each variable (amplitude, length and mass) and period of a simple pendulum. Give a brief description of the relationship below. a) Period and Amplitude b) Period and Length c) Period and Mass 2. How do your predictions compare with the results of your experiment? 3. Explore with the simulation how air resistance affects the period of a simple pendulum. Create and record your hypothesis, and verify your answer using the simulation. Move the friction toggle to the right. Hypothesis: Results: 4. If the pendulum set-up was transferred to the surface of the moon where the gravitational acceleration is 1/6 that of the earth, how should it affect the period of the pendulum? Verify your answer using the simulation. Select the moon radio button on the right side of the simulation page. Hypothesis: Results: Adapted from Simple Pendulum, Jay Gregorio, PhET
Part 2: Access and run the Masses & Springs PhET Simulation online at https://phet.colorado.edu/en/simulation/legacy/mass-spring-lab: 1. Determine how changing the mass on the spring changes the motion of the spring when hung from equilibrium on Spring 3. Mass Max displacement Period Frequency 50 g 100 g 2. How does the amount of mass affect the period of the spring? mass, longer period. mass, shorter period. 3. Next determine, with a constant mass of 50 g, how changing the "stretchiness" of the spring affects the period of the spring/mass system when hung from equilibrium. Stretchiness Max displacement Period Frequency Soft Medium Hard 4. How does the stretchiness of the spring affect the period of the spring? spring, longer period. spring, shorter period. 5. If you hang a mass on the spring and then pull the spring down further past the max displacement, how does the spring react? Does it move more quickly or more slowly? 6. How did this effect the period? mass, more speed; mass, less speed.
7. Select the box that will show the energy of spring #3. Observe what the graph looks like for the spring with medium stretchiness and the 50 g mass when hung from the equilibrium point. a.) When is KE the greatest? The least? b.). When is PE the combination of PE(gravity) and PE(elastic) - the greatest? The least? 8. For a 50g mass and medium stretchiness spring, sktech a graph of height of the mass over time. How can you find the amplitude and period from this graph? (Briefly explain) 9. From the data graphed above in step 8, sketch a graph of velocity and acceleration over time (do not worry about the scaling of the y axis, but keep the same scaling on the x axis from the previous graph) What would the amplitudes of the velocity and acceleration graphs represent? Adapted from Masses & Springs by Eric Aurand, PhET
Part 3: Testing Simple Harmonic Motion with a Spring. Use the spring and masses provided, along with some sort of timer (photogate or phone), to create your own experiment that will verify the relationship between period, spring constant, and mass: Things to consider: You will need to first figure out what k is for the spring you have chosen. How many data points will you need to establish this value? How uncertain will this be, and consequently, how uncertain will T be because of the uncertainty in k? You will need to time the motion of the mass on the spring. How many trials will you need to establish the period with precision? What methods could you use to do this? What are the advantages and disadvantages of each? Things to include in your abstract: You should have a hypothesis that you will be verifying, given the measured values for the variables involved. You should have results that support, or validate that hypothesis within experimental error and uncertainties, and you ll need to summarize those results in your abstract, including those uncertainties If your results for the measured period are NOT consistent with the equation, you ll need to explain why *briefly* in the abstact.