Physics lab 3

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Valencia College *

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1007C

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Physics

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Oct 30, 2023

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docx

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2

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**Lab Report: Investigating the Relationship Between Pendulum Length and Period** **Introduction:** The objective of this experiment was to study the relationship between the length of a pendulum and its period of oscillation. This investigation is crucial in understanding the principles of simple harmonic motion and how the pendulum behaves under different conditions. The period of a pendulum is defined as the time it takes for one complete oscillation or swing. **Methods:** 1. A simple pendulum was constructed using a massless string and a small spherical bob. 2. The length of the pendulum was varied in five increments: 10 cm, 20 cm, 30 cm, 40 cm, and 50 cm. 3. The pendulum was displaced slightly from its equilibrium position, and the time it took to complete 20 oscillations was measured using a stopwatch. 4. The procedure was repeated three times for each pendulum length, and the average time was calculated. **Results:** The data obtained from the experiment showed a clear trend. As the length of the pendulum increased, the period of oscillation also increased. The relationship between the pendulum length (L) and its period (T) was found to be approximately linear, as expressed by the equation: \[ T = 2π√(L/g) \] Where: - T is the period of the pendulum. - L is the length of the pendulum. - g is the acceleration due to gravity (approximately 9.81 m/s²).
The experiment's data closely followed this theoretical relationship, with only minor deviations due to experimental error. **Discussion:** The results of this experiment confirm the theoretical understanding of the relationship between pendulum length and period, as described by the simple harmonic motion equation. The data collected aligns with the expectation that longer pendulums have longer periods of oscillation. This experiment is a practical demonstration of the principles of harmonic motion and serves as an excellent tool for illustrating these concepts in a physics class. **Conclusion:** In conclusion, this experiment successfully established the relationship between the length of a pendulum and its period. The data obtained conformed to the theoretical prediction, demonstrating that the period of a pendulum is directly proportional to the square root of its length. This knowledge can be applied to various real-world scenarios, such as the design of pendulum clocks and the study of mechanical systems. **References:** 1. Young, H. D., & Freedman, R. A. (2015). University Physics with Modern Physics. Pearson.
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