1. The problem statement, all variables and given/known data 1. The first part of the problem was to find a transfer function. Output is the displacement of the mass (mass of pinion is negligible) 2.The next thing to do was find the poles, which I believe means set the denominator=0 and solve for s. 3. The next thing to do was find the damping ratio (z) and natural frequency (Wn) 4. Here is where I am stuck: Determine values of k and b such that the following are met: m=0.1kg r=0.01m 600msec<=rise time (tr)<=800msec and %OS <= 10% 2. Relevant equations The transfer function I came up with: 1. G(s)=(1/mr)/(s^2+b/m*s+k/m) Poles I found: 2. Poles=(-b/m +- sqrt((b/m)^2-4(k/m)))/2 3. z and Wn I found: z=b/(m*2*sqrt(k/m)) Wn =sqrt(k/m) 3. The attempt at a solution 4. To attempt to find values I used: Tr~1.8/Wn substituting into rise time equation (4) above I came up with 0.50625<=k<=0.9 I also concluded that z must be >= 0.6 for the overshoot condition. and solving (2) for b I have b>=0.12 *sqrt(k/m) I have tried rearranging these equations every way I can think of to come up with a solution. I have also tried making graphs by hand and using Matlab (though I'm not great with Matlab). The thing I am running into is that there seems to be any number of solutions that will work, but I am assuming that I am wrong and that there should only be one valid solution. Any help will be greatly appreciated, I've spent many hours trying to figure this out!