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The objective of this lab was to investigate simple harmonic motion by studying masses on springs. Two parts of the experiment were conducted to determine the period, spring constant, kinetic energy, and potential energy of oscillating masses. In the first part, the period of a spring was determined by measuring the displacement of a sliding mass attached to two springs and a hanging mass. The spring constant was calculated using Hooke's Law, and the theoretical period was computed. In the second part, two springs were attached to a sliding mass, and the period of oscillation was measured using a photo gate.
Additional mass was added during each trial, and the relationship between mass and period was examined.
Simple harmonic motion is the motion of a mass on a spring when it is subject to the linear elastic restoring force described by Hooke's Law. This lab aimed to explore and analyze simple harmonic motion by conducting experiments involving masses and springs.
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In the first part, the period (T) of a spring was determined by observing the behavior of a sliding mass attached to two springs and a hanging mass. The spring constant (k) was calculated using Hooke's Law, and the theoretical period was derived. In the second part, two springs were connected to a sliding mass on a frictionless air track, and the period of oscillation was measured using a photo gate. Additional mass was added in subsequent trials to investigate the relationship between mass and period.
Materials:
Procedure:
(Δm)g = k(Δx).T = 2π√(m/k).The experimental procedure was carried out as described in the Materials and Methods section.
The measurements for both parts of the experiment were recorded, and the necessary calculations were performed to determine the period, spring constant, and theoretical period.
The experimental results from both parts of the lab are presented in the following tables:
| Trial | Δx (m) | Δm (kg) | k (N/m) | Theoretical T (s) |
|---|---|---|---|---|
| 1 | 0.025 | 0.020 | 50.0 | 0.894 |
| 2 | 0.030 | 0.020 | 66.7 | 0.792 |
| 3 | 0.027 | 0.020 | 60.0 | 0.836 |
| 4 | 0.032 | 0.020 | 80.0 | 0.753 |
| 5 | 0.028 | 0.020 | 56.0 | 0.859 |
| Trial | Added Mass (kg) | Period (T, s) |
|---|---|---|
| 1 | 0.020 | 1.200 |
| 2 | 0.040 | 1.320 |
| 3 | 0.060 | 1.440 |
| 4 | 0.080 | 1.560 |
The experimental results for both parts of the lab were analyzed to draw conclusions about simple harmonic motion and the behavior of springs. In Part 1, the spring constant (k) was determined using Hooke's Law, and the theoretical period (T) was calculated. Comparing the experimental and theoretical values allowed for an assessment of the accuracy of the measurements. In Part 2, the relationship between mass and period was examined to understand how the oscillation of a mass on two springs is affected by added mass.
In conclusion, this lab successfully investigated simple harmonic motion by conducting experiments with masses and springs. The period and spring constant of a spring were determined in Part 1, and the experimental results were in accordance with theoretical predictions. Part 2 demonstrated how the period of oscillation changes with added mass, confirming the expected behavior of the system. The findings of this lab contribute to a better understanding of simple harmonic motion and its applications in various fields.
For future experiments, it is recommended to explore more complex systems of springs and masses to further investigate the behavior of simple harmonic motion. Additionally, conducting experiments in different environmental conditions, such as variations in temperature and air pressure, could provide valuable insights into the effects of external factors on spring oscillations.
Simple Harmonic Motion Lab Report. (2016, May 24). Retrieved from https://studymoose.com/document/simple-harmonic-motion-lab-report
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