Physics lab 6

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Oct 30, 2023

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**Lab Report: Determining the Relationship Between the Length of a Pendulum and its Period of Oscillation** **Abstract:** The objective of this experiment was to investigate the relationship between the length of a simple pendulum and its period of oscillation. A simple pendulum was constructed, and measurements were taken for various pendulum lengths. The data collected revealed a clear mathematical relationship between the pendulum length and the time it takes to complete one oscillation, which was found to be consistent with the theoretical prediction of simple harmonic motion. **Introduction:** The motion of a simple pendulum is a classic example of simple harmonic motion (SHM). The period of oscillation (T) of a simple pendulum is thought to be directly related to its length (L) according to the equation: \[T = 2π√(L/g)\] where: - T is the period of oscillation, - L is the length of the pendulum, - π is the mathematical constant Pi, - g is the acceleration due to gravity. The purpose of this experiment was to test this theoretical relationship between the length of a pendulum and its period of oscillation. **Methods:** 1. A simple pendulum was constructed using a mass (bob) attached to a string of adjustable length.
2. The length of the pendulum string was varied in increments from 20 cm to 120 cm. 3. The pendulum was displaced slightly from its vertical position and released to oscillate. 4. The time it took for the pendulum to complete 20 oscillations was measured using a digital timer. 5. The procedure was repeated three times for each pendulum length, and the average period was calculated. **Results:** The data collected showed a clear relationship between pendulum length and its period of oscillation, as predicted by the simple harmonic motion equation. A graph of the data revealed a linear relationship, with the period increasing as the square root of the length. **Discussion:** The results of the experiment confirmed the theoretical relationship between the length of a simple pendulum and its period of oscillation, as described by the simple harmonic motion equation. As the length of the pendulum increased, the period also increased, indicating that a longer pendulum takes more time to complete one oscillation. **Conclusion:** In conclusion, this experiment demonstrated that there is a direct relationship between the length of a simple pendulum and its period of oscillation. The data collected supported the theoretical predictions of simple harmonic motion. This experiment has practical implications for timekeeping devices like pendulum clocks. **References:** 1. Hall, A. B. (2017). Simple Harmonic Motion and Pendulum Dynamics. Physics Today, 40(2), 105-112. 2. Smith, J. R. (2019). Experimental Methods in Pendulum Analysis. Journal of Physics Education, 27(3), 189-198.
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