# Relationship between surface area and damping coefficient

1. Nov 16, 2014

### kucing

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/ [Broken]

Why is this the case? How can I explain this?

Last edited by a moderator: May 7, 2017
2. Nov 17, 2014

### Staff: Mentor

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