{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

4al Lab #6.8 - ± 0.001Hz We can see that the theoretical...

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

View Full Document Right Arrow Icon
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
Background 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 ]}