Relationship between surface area and damping coefficient

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SUMMARY

The investigation into the damping of an oscillating mass on a spring using a card of varying surface area revealed a non-linear relationship between the damping constant λ and surface area, contrary to the expected linear correlation. The method involved taking the natural logarithm of the amplitude of oscillations and plotting it against time to derive λ from the gradient. The results indicate that factors such as the geometry of the system and the mass of the card relative to the oscillating mass significantly influence the damping behavior. Further analysis is required to understand these complexities and their implications on the damping coefficient.

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  • Investigate the effects of geometry on damping in oscillatory systems
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kucing
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I have been investigating the damping of an oscillating mass on a spring by a piece of card of varying surface area, in order to work out the damping constant λ for the equation y = A₀ e-λt sin(ωt). I took the natural log of the amplitude of each successive oscillation and plotting that against time elapsed to give a graph of ln(y) = -λt + ln(A₀), so I could take the gradient and obtain a value for λ.

I then plotted a graph of my values for λ against the surface area of the card. I was expecting a linear relationship between λ and surface area, but instead obtained the non-linear graph I have attached.

https://www.physicsforums.com/attachments/screen-shot-2014-11-16-at-20-33-26-png.75536/

Why is this the case? How can I explain this?
 
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How exactly is the card attached to the mass? What is the geometry of the system? How does the mass of the card compare to the mass m? What do you get if there's no card attached?

Chet
 

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