example Pendulum Report

Introductory Physics Laboratory Faculty of Science, Ontario Tech University Lab Report IP-04: Oscillatory Motion of Simple Pendulum Examine the Position and Velocity Graphs Table 1 Run # m, kg L , m Δ x /2, m α 0 , rad/deg T E , s T T , s % diff 1 0.07 kg 0.95 m 0.1925 m 15 o 1.960 s 1.955 s 0.26% 2 0.07 kg 0.95 m 0.1195 m 10 o 2.000 s 1.955 s 2.25% 3 0.07 kg 0.95 m 0.085 m 5 o 2.000 s 1.955 s 2.25% 4 0.024 kg 0.95 m 0.137 m 10 o 2.000 s 1.955 s 2.25% 5 0.0137 kg 0.95 m 0.1275 m 10 o 2.000 s 1.955 s 2.25% 6 0.0075 kg 0.95 m 0.1035 m 10 o 2.040 s 1.955 s 4.16% 7 0.07 kg 1 m 0.1025 m 10 o 2.040 s 2.006 s 1.67% 8 0.07 kg 0.5 m 0.0790 m 10 o 1.480 s 1.418 s 4.19% 9 0.07 kg 0.25 m 0.0565 m 10 o 1.040 s 1.003 s 3.56% Examine the Kinetic and Potential Energy Table 2 Run # v m , m/s Δ x /2, m h , m U , J K , J % diff #1 0.596 m/s 0.1925 m 0.0197 m 0.0135 J 0.0124 J 8.15% Don’t copy just use as reference neither of us want a plagiarism offense Lab Report IP-04: Oscillatory Motion of Simple Pendulum

Introductory Physics Laboratory Faculty of Science, Ontario Tech University Examine the Phase Plane The difference in space between each phase plane is due to the different angles each pendulum was released at, the different angles caused different sizes of phase planes to be made with 5 o being the smallest and 15 o being the largest, causing different velocities and distance travelled. With 5 o having the lowest velocity and distance, and 15 o having the highest velocity and distance. Runs Run 1 Lab Report IP-04: Oscillatory Motion of Simple Pendulum 2

Introductory Physics Laboratory Faculty of Science, Ontario Tech University Conclusion: This lab was designed to explore the kinematic and dynamic properties of a simple pendulum's oscillation. The period of oscillation is measured using the position time graph. By varying the mass of the bob, the length of the pendulum, and the initial displacement, we aimed to understand their influence on the pendulum's period. The relationship between kinetic and potential energy was also analyzed. Our experiments demonstrated that the period of the pendulum varied with changes in the pendulum length and the initial angle, but not with the bob’s mass. This aligns with the theoretical model of a simple pendulum, where the period is independent of mass. The comparison between theoretical and experimental period values showed slight differences ranging from 0.26% to 4.19%, likely due to experimental errors such as air resistance, friction at the pivot point, and precision in measuring the period and angles. These values are still acceptable, as again they are both due to external influences and are negligible low amounts. In terms of both the pendulum mass and angle, these differences did not influence the period of the pendulum as they all had roughly the same T E and T T , however once the length of the pendulum changed the period changed as well, this is due to both gravity and length being a factor in period whereas mass and angle are negligible for period due to not being in any related equation. Lab Report IP-04: Oscillatory Motion of Simple Pendulum 4

Introductory Physics Laboratory Faculty of Science, Ontario Tech University The maximum potential energy of the pendulum in Run #1 was calculated using the equation U = mgh where m is mass (kg), g is gravity (9.8 m/s 2 ) and h is height (m), while the maximum kinetic energy was calculated using the equation K = m v m 2 /2 where m is mass (kg) and v m is the average velocity of the pendulum. This gave us a max potential energy of 0.0135 J and a max kinetic energy of 0.0124 J, an 8.15% difference. The use of velocity versus position graphs in the analysis part provides a visual representation of the pendulum's energy transformation, reaffirming the theoretical principles of energy conservation in harmonic motion. In conclusion, the lab successfully achieved its purpose. We learned about the factors affecting the period of a simple pendulum and gained practical experience in measuring and analyzing the kinetic and potential energies. The slight discrepancies between theoretical and experimental values highlight the impact of real-world conditions on idealized models, reinforcing the importance of considering external factors in experimental physics. Lab Report IP-04: Oscillatory Motion of Simple Pendulum 5