Lab Report - Simple Pendulum PDF

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Summary of the physics of a simple pendulum ...

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Simple Pendulum July 10, 2018 Avery Apanius & Jordan Crain Babu Gaire Jhena Smith

Abstract: A simple pendulum oscillation pattern is dependent on three variables that act on its motion. Its mass, length, and amplitude are capable of changing the pendulums pattern. In this experiment these variables are tested to obtain an understanding of their role in this system. Each variable will alter the pendulum pattern in a unique way such as elongating or compressing the oscillation period. Introduction: The goal of this experiment was to apply physics principles to a simple pendulum scenario that altered length, mass, and initial angle of motion (amplitude). Data from these tests will be analyzed in order to gain an understanding of the manipulated variables. The data will be in the form of graphs that can show the relationship between the alterations. The graphical component of these tests depends on the period of oscillations measured by a rotary motion sensor. The sensor will record into a program called PASCO ScienceWorkshop 750 interface. Theory: The main equation used through this experiment is T = 2 Sqrt (l / g), which is a simple harmonic oscillator calculation. As you can see, the components of mass, length, and angular motion can be manipulated through this equation. In order to limit error, the rod that is used must be of light weight in order for it to be negligible except when mass is added. A protractor can be used to place the pendulum at the proper angle to increase accuracy of the test. In theory, each manipulation of a variable should yield a new result. It is this information that can be analyzed for patterns. Procedure: For a proper experiment, begin by assembling an apparatus with a rotary sensor attached to a

simple pendulum attached to a massless block. The procedure will be repetitive in order to obtain three valid tests for each testable variable of mass, length, and initial angle of motion (amplitude). Begin by manipulating length of the pendulum, this test will initially start at the full length possible. Then, record all data of the oscillation test into the computer program. This graph will be printed in order to display the data for the test. Repeat these steps for 2 other variable lengths. Then manipulate the next variable of mass using weighted blocks to simulate a heavy mass at the end of a simple pendulum. Again, record all data, print the data, and repeat for two different masses to obtain three total mass tests. Lastly, place the simple pendulum, with original mass and length, at variable angles in order to obtain three variable angle tests. Data: Tests #1-3 ∆

= 30 = 60 = 90

Tests #4-6 ∆Mass

M= 0kg M= 0.1kg M= 0.2kg

Tests #7-9 ∆L

Mass=0

L= 0.412m

= 30

L= 0.412m

= 30

Mass= 0kg

L= 0.412m L= 0.271m L= 0.136

Graphs: See graphs attached at the end of the lab report (Test #1-9) Calculations: As you can see from the provided equation from the theory section of this lab report, we used T=2 Sqrt (l /g ) for this experiment. This is how you calculate the period of oscillation for a simple harmonic oscillator. Simple pendulums include 3 main factors that can be manipulated that are L for length of the pendulum, M for mass at the bottom of the string, and theta () for the initial angle of the pendulum when we let go of it. As indicated by the given equation for the period of oscillation the only undefined factors are g for the acceleration rate based off of gravity

and L for the length of the string of the pendulum. Based off of this information, it goes to show that of all three factors (, M, L) only the length of the rope has an effect on the period of oscillation. For example, for tests 7, 8 and 9 where we varied the lengths of rope the period of oscillation was 1.28 sec, 1.04 sec and 0.740 sec, respectively. Conclusions: This experiment was intended to investigate and discover what aspects or factors influence or effect the period of oscillation of a simple pendulum. We were able to alter and adjust various factors such as mass, length of the rope, and the initial angle that the pendulum is dropped at. After testing the period of oscillation while varying each factor, we discovered that the period of a simple pendulum is dependent on the length of the pendulum. It is the factor that can increase or decrease the period of a pendulum. Ultimately, all other factors, mass and angle, have no effect on the period whatsoever. This is also clear to tell because length is the only factor other than gravitational acceleration that are included in the equation used to calculate the period of oscillation....