# Calculate viscous damping coefficient given force

With a force metre I recorded the force vs time of a spring with a disk on the end in water, experiencing viscous damping, during damped oscillatory motion. I pulled the disk to the bottom of the container of water then let go allowing it to move for 25 seconds. Force is at the maximum when the disk is lowest.

How can I determine the viscous damping coefficient? Normally these graphs use distance and velocity but I only have force.

My equation force is of the same form as the one for motion:

$$x(t) = Ae^{-bt/2m}\cos(\omega't+ \phi)$$

The three forces are buoyancy, viscous drag and elastic. Buoyancy could be neglected if it simplifies things.

• Total mass of object: 0.714 kg
• Surface area of disk: 254 cm^2

Here is a graph of my data, cut to the start with the exponential function plotted.

• If you know the force the spring exerts you know the position of the disk overtime, and hence its velocity over time, don't you? – Aaron Stevens Jul 31 at 16:00
• @AaronStevens I assume you're referring to hookes law. However, my understanding is that because of the force due to drag the force recorded by the force metre is not proportional to distance. The force on the graph is a combination of viscous drag force and spring force. – Joe Clinton Jul 31 at 16:06
• You are right that the total net force is not proportional to distance. But you aren't measuring the net force. You're just measuring the spring force, right? – Aaron Stevens Jul 31 at 16:08
• My setup is a force metre attached to a tripod with a spring on the end. Then on the end of the spring is a disk with weights. The disk and weights go in a beaker of water. The force metre records how much the spring system pulls on it. I believe that if the spring is moving through the water there will be a force that the spring applies to the mass and a force opposite to that the water applies. I think the force metre records net force but I might be wrong. I will create a diagram and add it to the question. – Joe Clinton Jul 31 at 16:15
• @AaronStevens I have added a diagram, are you sure that the force measured by the force metre is only the force exerted by the spring and thus proportional to distance? – Joe Clinton Jul 31 at 16:43