4al Lab #6.8 - As seen in the graphs the undamped...

Info icon This preview shows page 1. Sign up to view the full content.

As seen in the graphs, the undamped oscillations were did not vary much in amplitude. The 50mm and 20mm magnet gaps resulted in underdamped systems. The 13.5mm gap was close to the critical damping. And the 10mm and 5mm magnet gaps were examples of overdamping. The closer the magnets were to the pendulum, the more damping force on the system. Analysis of Undamped Frequencies: Theoretical Frequency Experimental Frequency Absolute Difference Percent Difference 0.7144 ± 0.002 Hz 0.7109 ± 0.001 Hz 0.0035 Hz 0.4899% 𝑓 ? ?ℎ = 1 2𝜋 ??? 𝑐? ? 1 2𝜋 0.1716∗9.8∗ .3816 0.0321 = 0.7144 ± 0.002 Hz σ f u = ( ∂f u ∂m ) 2 σ m 2 + ( ∂f u ∂k ) 2 σ k 2 ( ∂f u ∂m ) 2 0.025 + ( ∂f u ∂k ) 2 0.025 = 0.002 Hz s s s T 406 . 1 6 48 . 0 92 . 8 𝑓 ? 𝑒𝑥𝑝 = 1 𝑇 = 1 1.406
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ± 0.001Hz We can see that the theoretical result does not differ much from the experimental result which is accurate. The experimental frequency was calculated using the time between each of the successive peaks of oscillation from the graphs. “Q” for the oscillation with a 50mm magnet gap: ¾ ¿ = À ÁÂà À Á Formula to calculate amplitude ratios with the Ä ÅÆ peak on the graph. Ç ¿ = − ² 2ln ÈÉ Á Ê Quality Factor from amplitude ratios Ç = ± Ë ∑ Ç ¿ Ë ¿Ì± Overall Quality Factor Value for “n” ¾ ¿ Ç ¿ 1 0.9444 ± 0.0022 27.459 2 0.9608 ± 0.0027 39.281 3 0.9388 ± 0.0025 24.873 4 0.9565 ± 0.0031 35.319 5 0.9555 ± 0.0028 34.507...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern