Lab Report #11

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School

Florida International University *

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Course

2048L

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Physics

Date

Dec 6, 2023

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pdf

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Uploaded by AdmiralFlowerSardine36

Isabel Ruiz 6353644 Jonathan Fernandez 6207792 Orlando Haya-Cuan 6309952 Lab Report #11 Preliminary Questions 1. Attach the 200 g mass to the spring and hold the free end of the spring in your hand, so the mass and spring hang down with the mass at rest. Lift the mass about 5 cm and release. Observe the motion. Sketch a graph of position vs. time for the mass. 2. Just below the graph of position vs. time, and using the same length time scale, sketch a graph of velocity vs. time for the mass. 3. Measure the spring extension when you hang the 200 g mass and calculate the spring constant, k. Then calculate the theoretical frequency with which the system will oscillate. K=-F/x K=-mg/x K=0.2kg x 9.8/0.1m K=19.6 Procedure 1. Attach the spring to a horizontal rod connected to the ring stand and hang the mass from the spring, as shown in Figure 11. 1. Securely fasten the 200 g mass to the spring and the spring to the rod, using twist ties so the mass cannot fall. Adjust the height of the mass so that the bottom of the mass is about 33-55 cm from the table top or floor. 2. Set the Motion Detector sensitivity switch to Ball/Walk. Connect the Motion Detector to a digital (DIG) port of the interface. 3. Place the Motion Detector below the mass. No objects should be near the path between the detector and mass, such as a table edge. Place the wire basket over the Motion Detector to protect it. 4. Open the file "Simple Harmonic Motion" from the Lab 11 folder. 5. Make a preliminary run to verify things are set up correctly. Lift the mass upward a few centimeters and release. The mass should oscillate along a vertical line only. Click • Collect to begin data collection. 6. When data collection is complete, the position graph should show a clean sinusoidal curve. If it has flat regions or spikes, reposition the Motion Detector and try again.

7. Compare the position graph to your sketched prediction in the Preliminary Questions. How are the graphs similar? How are they different? Also, compare the velocity graph to your prediction. ● The graph is really similar in the fact that both oscillate and each oscillation looks identical. The biggest difference is that the graph I drew in the preliminary questions does not oscillate as much as the actual graph. 8. Estimate the equilibrium position of the 200 g mass. Do this by allowing the mass to hang free and at rest. Click D Collect to begin data collection. After collection stops, click Statistics, W, to determine the average distance from the detector. Record this value as position (%) for Run 1 in your data table, Table 11.1. 9. Now lift the mass upward about 5 cm and release it. The mass should oscillate along a vertical line only. Click D Collect to collect data. Examine the graphs. The pattern you are observing is characteristic of simple harmonic motion. 10. Use the position graph to measure the time interval between maximum positions. This is the period, T; of the motion. For improved accuracy, measure the time interval between, say, the first and eleventh maxima and divide this by 10. (There are 10 periods between the first and eleventh maximum.) The frequency, J, is the reciprocal of the period, J = 1/1. Based on your period measurement, calculate the frequency. Record the period and frequency of this motion in your data table, Table 11.1. 11. The amplitude, A, of simple harmonic motion is the maximum distance from the equilibrium position. Estimate values for the amplitude from your position graph. Enter the values in your data table, Table 11.1. If you drag the mouse from a peak to an adjacent trough, Logger Pro will report the change in position over that region. 12. Repeat Steps 9-11 with the same 200 g mass, but with a larger amplitude than in the first run. 13. Change the mass to 300 g and repeat Steps 8-11. Use an amplitude of about 5 cm. Keep a good run made with this 300 g mass on the screen. You will use it for several of the Analysis questions. Analysis 1. View the graphs of the last run. Compare the position vs. time and the velocity vs. time graphs. How are they the same? How are they different? The biggest similarity is that both oscillate and oscillate the same amount of times during a given time frame. The biggest difference is the placement of the waves. For the velocity, it crosses the x axis meaning it has a positive and negative value while the position is always positive. Another difference is that the velocity is shifted more to the right than the position graph. 2. Click Examine, , to use the Examine tool. Move the mouse cursor back and forth across the graph to view the data values for the last run on the screen. In your data table, Table 11.2, record time and position values for when v = 0. Also, record time and position values for a point when the velocity is greatest. Relative to the equilibrium position, where is the mass when the velocity is zero? Where is the mass when the velocity is greatest? When the velocity is 0 the mass is at its local maximum or local minimum. When the velocity is at a maximum The mass is in the middle of rising.

3. Does the frequency, f, appear to depend on the amplitude of the motion? Do you have enough data to draw a firm conclusion? No, the frequency did not depend on the amplitude. We say no relationship between the two since when the amplitude decreased from run 2 to 3 it had no effect on the frequency. 4. Does the frequency, J, appear to depend on the mass used? Did it change much in your tests? Yes, the frequency depended on the mass of the object. In tests 1 and 3 both masses we released 5 cm from rest and the only difference was the masses of the objects. When comparing the frequency, the frequency had changed by 1/0.2 Hz. 5. How does the frequency with the 200 g mass compare with the theoretical value that you obtained in Preliminary Questions? No, the frequency had no impact on the amplitude. This can be seen from Table 11.1's data, which demonstrates that although the amplitude varies between Runs 1 and 2, the frequency remains constant. This is also in line with the simple harmonic motion mathematical model, which indicates that the frequency is independent of the amplitude and only dependent on the mass and spring constant. 6. You can compare your experimental data to the sinusoidal function model using the Model feature of Logger Pro. Try it with your 300 g data. The model equation in the introduction, which is similar to the one in many textbooks, gives the displacement from equilibrium. However, your Motion Detector reports the distance from the detector. To compare the model to your data, add the equilibrium distance to the model; that is, use y = Asin (2mft + $) + Yo where yo represents the equilibrium distance. The phase parameter, , is called the phase constant and is used to adjust the y value reported by the model at t = 0 so that it matches your data. a. Click once on the position graph to select it. b. Choose Model from the Analyze menu and select Latest. c. Select the Sine function from the General Equation list. d. The Sine equation is of the form y=A*sin(Bt +C) + D. Compare this to the form of the equation above to match variables; e.g., $ corresponds to C, and 2rf corresponds to B. e. Adjust the values for A, B and D to reflect your values for A, f and yo. You can either enter the values directly in the dialog box or you can use the up and down arrows to adjust the values. f. The optimum value for will be between 0 and 2n. Find a value for f that makes the model come as close as possible to the data of your 300 g experiment. You may also want to adjust yo› A, and to improve the fit. Write down the equation that best matches your data. 7. Does the model fit the data well? How can you tell? The data fit the model well. With relatively little scatter, the model curve is nearly completely superimposed on the actual points. This suggests that the link between the mass's position and time is accurately portrayed by the model.

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