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Daniel Sellers

- 117

- 17

## Homework Statement

Hello all,

I have a question regarding the damping constant for a model of a vertically oscillating mass on a spring. I have read through one or two similar questions on this site but I think I can manage to be a little more specific about what I'm asking.

I am in a physics lab course and have collected data from a motion detector for a mass on a spring by itself, and two sets of data for which wide, flat objects were affixed to the mass (with some metal disks removed from the mass to offset the additional mass from the 'damper').

I am asked to create a theoretical model for the equation of motion and compare it to our collected data. The issue I'm having is when I try to predict the damping constant, b. I am hoping to find an expression for drag force which is linear with respect to velocity; the constant be needs to be such that multiplying it by v gives units of force.

The model of drag force I have learned previously is dependent on (v^2)/2 and so throws off my model. I have looked into Stoke's equation since our system never reaches very large velocity, but treatments of Stoke's seem to specify that it applies only small spherical objects moving slowly enough that the airflow relative to the object is completely laminar.

So my question is this; is there a way predict b (even with somewhat low accuracy) from the area and possibly an average velocity which gives be in units of kg/s? or alternatively, is there a way to take the fairly simple drag force equation [(CA{rho}v^2)/2] and make it dependent on v instead of v^2?

Or any other ideas for how I might make a reasonable guess at b for the sake of creating a theoretical model to compare my data to. I am not versed in fluid dynamics beyond the basics like Bernouli's and the equation of continuity for laminar flow, but I will make every attempt to learn the necessary math and physics if someone could point me in the right direction.

2. Homework Equations ; unknown (or stated above)

3. Attempt at the solution;

Algebraic manipulation and seemingly endless forum searches.