Phys 244 Simple pendulum Online Fall 2022 (4)

George Mason University Physics 244 (Online) Simple Pendulum RESULTS Group Lab Report * Title of Experiment: Harmonic Motion Date: 11/12/23 Class, Section & Lab group: Phys 244 2D1 Group 5 Recorder (consolidates report and submits into dropbox): Robert Orellana-Alvarez Group Members PRESENT Robert Orellana-Alvarez, Rebecca Turcios * Before beginning, save this report on your desktop with the Recorder's last name appended. 1 Figure 1: Pendulum - an example for harmonic motion

Figure 2: Motion of a pendulum and forces acting on it. Table 1: Period of a pendulum with varying horizontal displacement Trial Angle (deg) Period (s) 1 5 1.6792 2 10 1.6816 3 15 1.6856 4 20 1.6913 5 25 1.6986 6 30 1.7076 7 35 1.7184 8 40 1.731 Table 2: Period of a pendulum with varying mass Trial Bob Mass (kg) Period (s) 1 0.2 1.6856 2 0.5 1.6856 3 0.8 1.6856 4 1.1 1.6856 5 1.4 1.6856 Table 3: Period of a pendulum with varying arm length Trial Pendulum Arm Length (m) Period (s) √( ) 𝑃𝑒𝑛𝑑𝑢𝑙𝑢𝑚 𝐴𝑟𝑚 𝐿𝑒𝑛𝑔𝑡ℎ (m^1/2) 1 1 2.0147 1 2 0.8 1.802 0.894427191 3 0.6 1.5606 0.774596669 2

Graph 3: Period (s) on y-axis vs √(𝑃𝑒𝑛𝑑𝑢𝑙𝑢𝑚 𝐴𝑟𝑚 𝐿𝑒𝑛𝑔𝑡ℎ ) (m^1/2) on x-axis for values in Table 3 1. Did changing the mass of the pendulum bob affect the period of the simple pendulum? Justify your answer. The period of a pendulum is independent of the mass of its bob. This phenomenon may be understood in terms of Newton's second law. The force is exactly proportional to the mass in F = m a. The force on the pendulum rises with mass, but acceleration doesn't change. The force of gravity is to blame. 2. Did changing the length of the pendulum arm affect the period of the simple pendulum? Justify your answer. A simple pendulum's period is only determined by its length and the acceleration brought on by gravity. Mass and other variables have no bearing whatsoever on the timeframe. 3. Keep the angle, mass and length constant. Choose and angle to 15 degrees, set the mass to 1 kg and the length to 1m. Now change the gravity (Moon, Earth and Jupiter) and record the period. How does the period depend on gravity? For Earth and Jupiter, the periods are about the same. For the gravity of the Moon, the period was four times longer than Jupiter. 4. For each part of your experiment, list each variable involved and state whether it was held constant, increased, or decreased. In your experiment, what variables (physical properties) affected the period of a simple pendulum and how ? The mathematical equation describing the period Tp of a pendulum is: 4

(3) where l is the length of the pendulum arm and g is earth’s gravitational acceleration constant. Does your data support this mathematical relationship? Justify your answer. An increase in angle degree increased the period of the simple pendulum, when pendulum arm length, gravity, and mass were constant. An increase in bob mass resulted in a constant period if the pendulum arm length, gravity, and angle remained the same for all measurements. A decrease in pendulum arm length caused a decrease in the period of the simple pendulum, when the angle, gravity, and mass were constant. An increase in gravity caused the period to decrease if all other factors were constant. The angle degree and pendulum arm length had a positive correlation with the period, while gravity had a negative correlation. The data does not support the mathematical relationship, because the angle of the of period Tp of a pendulum is not included. The exclusion of mass in the equation is acceptable, because the mass had no effect on the period. The inclusion of pendulum arm length and gravity is supported by the data as both factors had an impact on the pendulum period. The only exception is the angle, which also influenced period time, so the mathematical relationship is only supported for a harmonic motion measurement if the angle is added, or small similar sized angles are measured. Conclusion: Based on our experiment, we agree with the hypothesis that states that for a simple pendulum (T = 2pi sqrt(L/g)), a pendulum's period is mostly dependent on length. But only modest angles—roughly five or less—will work with this. It is observed that at bigger angles, the pendulum moves more slowly than the simple pendulum hypothesis. The sole angle at which we tested the mass dependency was angle 5, and at that angle the period does not rely on the mass. 5