How to calculate the viscous damping coefficient given drag force

Question

Force due to drag at low velocities, is equal to some constant times negative velocity

$$F_{d}=-c_{1}V$$

The viscous damping coefficient equals decay constant divided by 2 times mass

$$gamma = frac{c_{2}}{2m}$$

So, is $c_{1}$ the same as $c_{2}$?

How is the drag force related to the viscous damping coefficient, what equation is there to relate them?
I think the relationship is linear but I'm not certain.

For context, this is for a mass-spring system inside a beaker of water being damped by the friction of the water.

kamran · Answer

What you have is not actually fully submersed drag equation, or else it would be correct to handle it as damping.
The drag force on a submersed streamlined object is:$$ F_D=frac{1}{2} rhocdot u^2C_DA  $$

$F_{D} = $  the drag force

$ rho=$ mass density of the fluid

$ u= $ the flow velocity

$C_D= $ the drag coefficient (function of the Reynold's number)

$A=$  is the crosssectional  area

How to calculate the viscous damping coefficient given drag force

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