lab report 4

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East Carolina University *

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1251

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Physics

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Dec 6, 2023

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What is a Small-Angle Period? Section 1 In the guiding question, it asks what is the nut position for which the pendulum small-angle period is minimum? In order to answer this question we need to calculate the period. A period is the time it takes for an object to complete one cycle of oscillation. An oscillation is the swing of a pendulum until it reaches its initial starting position. To find the minimum small angle period, the length of the pendulum and the force of gravity needs to find a balance, minimizing the time it takes for the pendulum to complete its oscillation cycle. This scientific experiment aims to pinpoint the precise nut position that optimizes the pendulum’s efficiency by minimizing the interval between oscillation cycles. Section 2 In order to collect our data, a pendulum was set up with 5 nuts that acted as an anchor to allow our rod to swing. The distance from the base of the rod to the 3rd nut was measured and incremented by 0.05m. At each distance, starting from 0.05, 10 oscillations were timed and recorded into an Excel. We continued to time the oscillations up till 0.50m. The measurement with the least time was observed and, in order to find the true small-angle period, expanded to measure values between 0.15 and 0.20. We then used data analysis to create a scatterplot that displayed a near parabola. This
What is a Small-Angle Period? showed us our true lowest small-angle period. We calculated the period using the following equation: T = time ( sec ) ¿ oscillations We then calculated the period of a simple pendulum using the following equation: T = 2 π √ L / g Then in order to convert the period of a simple pendulum we had to give a linear relationship to the pendulum length (L) and the period (T), we squared both sides to give us the following equation: T 2 = 4 π 2 g L Using the above equation, we were able to calculate the gravity that acted on our pendulum swing. In order to reduce error, we ensured that the pendulum was swinging back and forth. When the pendulum would begin to swing in a circular motion, we would discard the data and redo the oscillation count. Section 3 Our claim to the guiding question was that the small angle period was observed when the nut position was 0.15m from the base of the pendulum. In order to calculate this claim, we expanded on the measurements of the nut positions between 0.15m and 0.20m. We then calculated the periods and
What is a Small-Angle Period? found the lowest value and determined that to be our small-angle period that is minimum. The small angle period showed us at which length the pendulum will swing the full 10 oscillations in the fastest time. The limitation of our measurements were attributed to the inability to get a consistent swing of our pendulum, which may have affected the time recording of each oscillation, making the recording slower than it should’ve been. We seemed to be the outlier group as most other groups received results within the 0.20m and 0.25m.
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