Lab#11 Simple Harmonic Motion

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School

Florida International University *

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2048L

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Physics

Date

Dec 6, 2023

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pdf

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Uploaded by JusticeFreedomLyrebird27

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.

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 position-time graph and the velocity-time graph from the preceding trial share characteristics, including a sinusoidal nature and an identical time interval. The position graph exhibits a more gradual curve compared to the velocity graph. Velocity reaches its maximum when the position is at the equilibrium point, and velocity is zero when the position hits its amplitude value. The initial position is marked by a y0 value, while the initial velocity is 0 m/s, reflecting the initial state of rest for the masses. 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, 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 reaches zero, the mass is at its farthest point from the equilibrium position, or at its maximum amplitude. Conversely, when the velocity is at its peak, the mass is in a state of equilibrium. 3. Does the frequency, f, appear to depend on the amplitude of the motion? Do you have enough data to draw a firm conclusion? Through multiple experimental runs, it was observed that the frequency does not seem to be influenced by the amplitude of the motion. In both runs, despite a change in amplitude from 0.4879m in run 1 to 0.5046m in run 2, the frequency remained constant at 1.3466Hz. It's important to note that the limited dataset, comprising only two runs with the same mass, prevents a definitive conclusion. However, even with additional runs, it would likely become evident that the frequency is independent of the amplitude of the motion.

4. Does the frequency, f, appear to depend on the mass used? Did it change much in your tests? The frequency seems to be influenced by the mass employed in the experiments. In one set of experimental runs, using a system mass of 200g yielded a frequency of 1.3466Hz. Subsequently, when the mass was increased to 300g in another run, the frequency dropped to 1.0823Hz. Although the observed change in frequency during testing was relatively modest at 0.2643Hz, it was significant enough to indicate a dependence of frequency on mass. 5. How does the frequency with the 200 g mass compare with the theoretical value that you obtained in Preliminary Questions? The calculated frequency for the 200g mass in both runs 1 and 2 was 1.3466Hz. In the preliminary questions, I established a theoretical frequency of 2.228Hz. A comparison reveals that the theoretical frequency exceeded the observed frequency. The disparity between the theoretical and experimental frequencies amounted to 0.8814Hz, representing a substantial 49.323% difference between the two results. 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(2(pi)(f)(t) +Ø)+ y0 where y0 represents the equilibrium distance. The phase parameter Ø 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. The equation that best matches the data is: -0.06676*sin(7t+1)+0.25 7. Does the model fit the data well? How can you tell? The model demonstrates a strong fit to the data with coefficients A: -0.06676, B: 7, C: 1, D: 0.25. This is evident as the differences between observed and predicted values are minimal and unbiased. Both the graph in the previous question and the one below illustrate that the model almost entirely aligns with the collected data, with only a minor discrepancy observed towards the end of the graph.

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