Lab 10Physic Subash

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Berkeley City College *

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Physics

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Jan 9, 2024

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Subash Thapa Physics 4A Professor Monsalve Lab 10: Simple Harmonic Motion Procedure: The experiment commenced with the assembly of the apparatus by securely attaching the spring to the horizontal rod connected to the ring stand, followed by suspending a 200 g mass from the spring, ensuring its firm attachment using twist ties. The height of the mass was meticulously adjusted within the range of 35–55 cm from the tabletop or floor to maintain consistency in the experiment. The LabQuest device was employed by connecting the motion detector and initiating a new project, configuring the motion detector to Ball/Walk mode for sensitivity. Ensuring an unobstructed path, the motion detector was positioned directly beneath the suspended mass, covered with a protective wire basket to prevent any potential damage. A preliminary trial was conducted, lifting the mass slightly and releasing it to ascertain smooth vertical oscillation while keeping a safe distance of at least 15 cm from the motion detector. Subsequently, data collection was initiated, and the resulting position vs. time and velocity vs. time graphs were examined to ensure the expected sinusoidal patterns and minimal aberrations. Comparison between the observed graphs and anticipated patterns was made, and the equilibrium position, period, frequency, and amplitude of the oscillation were estimated based on the collected data. Following this, additional runs were performed with variations in mass (200 g and 300 g) and amplitudes while maintaining a controlled and observable motion range to explore the effects of these variations on the oscillation patterns and measurements. Data

Subash Thapa Physics 4A Professor Monsalve Data Table 1: Run Mass (g) Y(initial) (m) A (m) T (s) f (Hz) 1 148.0 g 0.749 m 0.05 m 0.65 sec 1.538 Hz 2 148.0 g 0.753 m 0.10 m 0.65 sec 1.538 Hz 3 295.4 g 0.629 m 0.05 m 0.95 sec 1.053 Hz 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? In Run 3, the position vs. time and velocity vs. time graphs are very similar. They follow the same oscillation pattern, however the velocity graph has its maximum when the position graph is a little less than zero. When velocity is at its minimum, the position graph is at the same point of a little less than zero. Another difference is that the minimum Y value for the position graph is -0.68 m, and the minimum velocity Y value is more like -0.30m. 2. Record time and position values for when velocity = 0, and when velocity is the greatest. Data Table 2: Time (sec) Position (m)

Subash Thapa Physics 4A Professor Monsalve When v = 0 1.70 sec -0.794 m When v is maximum 1.85 sec -0.756 m 3. Does the frequency appear to depend on the amplitude of the motion? Do you have enough data to draw a firm conclusion? No, the frequency does not appear to depend on the amplitude of motion. From the minimal data we have this conclusion is clear, however a firm conclusion could be drawn if we had conducted more trials. 4. Does the frequency appear to depend on the mass used? Did it change much in your tests? Yes, our results show that the frequency depends on the mass used. The frequency was approximately 1 Hz with the roughly 300g mass, as opposed to 1.5 Hz with the roughly 150g mass. 5. Fitted equation with parameters: y = Asin(Bx + C) + D A: 0.041 B: 6.766 C: 0.691 D: -0.629 This model fits our data well. We can tell because it follows the graph we were given for Run 3. If we double the amplitude, the maximum and minimum values are much higher in alignment with the larger amplitude. Calculations

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Subash Thapa Physics 4A Professor Monsalve T = 2pi(sqrt(m/k)) B = 2pi(f) f = B/2pi → Hz f = 1/T Y = Asin(2pi(f)(t)) → Simple Harmonic Motion Y = Asin(Bx + C) + D → Fitted equation Source of Error: Certainly, in this experiment, there were several potential sources of error to consider. Human error played a significant role, particularly in the setup of the apparatus, where precision was crucial for obtaining accurate results. Any misalignment or errors in setting up the apparatus, particularly in relation to the spring and motion detector, could have introduced significant inaccuracies into our findings. Additionally, while lifting the mass to different heights, it was challenging to ensure precise measurements of 5cm or 10cm increments consistently. Moreover, the motion of our hand during the lifting process could have unintentionally influenced the data collected by the motion detector if there was any horizontal movement instead of solely vertical motion. The reliance on technological tools, such as the LabQuest device and motion detector, introduced another potential source of error. Any malfunction or technical issue with these devices could have skewed the collection of motion data, impacting the accuracy of our results. Furthermore, the integrity of the spring used in the experiment was crucial. If the spring was defective, warped, or improperly manufactured, it might not have operated as expected, affecting the vertical motion that was essential for the experiment.

Subash Thapa Physics 4A Professor Monsalve Considering the complexity of the setup involving multiple components and the likelihood of human error, there existed numerous potential sources of error that could have affected the precision and reliability of our experiment. Conclusion: In our laboratory investigation, we explored the predictable motion of a 200 g weight suspended from a spring, observing its oscillations. Employing a motion detector linked to LabQuest, we meticulously gathered data to validate the functionality of our setup. By analyzing graphical representations of the weight's movement across time, we ensured it adhered to the anticipated smooth and rhythmic pattern. Any discrepancies in the graphs prompted us to fine-tune the motion detector for accuracy. Our assessment involved aligning projected outcomes with observed occurrences. Identifying the equilibrium point—the weight's preferred position—we calculated its maximum and minimum displacement (amplitude) and frequency of oscillation. Our results indicated a correlation between alterations in weight and displacement, influencing the frequency of swings. Notably, the introduction of a heavier weight (300 g) induced distinct changes compared to using a lighter one (200 g). To sum up, our experiment illuminated the predictable nature of motion, demonstrating the interconnectedness of weight, displacement, and oscillation frequency. The successful setup validation and congruence between our anticipated and actual results solidified our experiment's reliability.

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