1. The problem statement, all variables and given/known data I have a transfer function in the laplace domain, and I have been asked to: "Develop Relationships in terms of the constant parameters and adjust K such that the constants are: A = 2, B = 1, C = 3, a = 3, b = 1" After finding this relationship, I am asked to convert it back to time domain, find damped natural frequency, and adjust K for critical Damping. I drew up this graph in MSpaint, sorry about the terrible quality, but it should hopefully be enough to get the general drift. As far as i can tell it's a graph of the response (laplacian?) against the undamped natural frequency multiplied by time, and it looks like a decaying cosine function. (at least the original does!). 2. Relevant equations Transfer function (Laplace Domain) = K/[(s+a)(s+b-A.B)+K.C.B] 3. The attempt at a solution I derived the Transfer Equation from a block diagram that I was given, and I am confident that I got that part correct. I'm not sure what this question means by "develop relationships in terms of the constant parameters and adjust K such that the constants are... etc" , because as far as I can tell, the constants are not actually related to each other, and the Value of K has no bearing on what the other constants will be, right? Following this, the rest should be fairly straightforward: 1) Convert back to time domain using the Laplace transform table, 2) Find my damped natural frequency from measuring periods on the graph. 3)Arranging the equation into (D^2)/(omega^2) + D(2.E/omega) + 1 where D = differential operator, omega = undamped natural freq, E = damping ratio. Substituting natural frequency found in 3, and then making E = 1 for critical damping, to find the adjusted K value. TL;DR - What is being asked in the phrase "Develop Relationships in terms of the constant parameters and adjust K such that the constants are: A = 2, B = 1, C = 3, a = 3, b = 1"? Should I substitute the constants into the equation, and find the equations for s? Please help me! I've been stumped on this all week and can only feel myself getting stupider!!