1. The problem statement, all variables and given/known data Hi everyone! I'm still trying to make my way through the wonderful land of oscillations. That's gonna take a while. The springs and shock absorbers of a small truck have been conceived, so that the truck body sinks of a distance s = 100mm by full load (total mass m = 1.8 t) and that the wheels (mass mR = 40 kg) oscillate in aperiodic damping. The four wheels carry the same amount of weight and each wheel has its own spring and shock absorber. Consider a general damping force FR = -b⋅v. How big must the spring constant k and the friction constant b of a shock absorber be? 2. Relevant equations Newton, oscillations 3. The attempt at a solution I attempted to solve this old homework using what another student did. There are a few obscure points I'd like to ask your opinion about, so that I can better understand them. Please check the attached photo to have a visualisation of how I conceive the situation in my head. I would like to start with a question: does "aperiodic damping" refer to "critically damped"? I translated the problem from German, so I'm not sure but that's what I assumed when solving the problem. So first I think that by full load and no oscillation, the forces of gravity (I named F'g the force of gravity acting on one wheel) and spring are balanced and there is no damping force: ΣF = 0 ⇔ F'g = FF ⇔ ¼⋅m⋅g = -k⋅s I solve for k: k = m⋅g/4⋅s = 44100 N⋅m-1 To get b, I thought the first thing to do was to set up an equation of motion for one wheel: mR⋅a = ¼⋅m⋅g + k⋅x - b⋅dx/dt ⇔ mR⋅d2x/dt2 + k⋅s - k⋅(x + s) + b⋅dx/dt = 0 ⇔ mR⋅d2x/dt2 + k⋅x + b⋅dx/dt = 0 ⇔ d2x/dt2 + (k/mR)⋅x + (b/mR)⋅dx/dt = 0 Hopefully this is correct. Now I saw on wikipedia that the next step is to define the natural frequency ω0 = √(k/mR). Why do we do so? Do we really define it? Anyway I can then write the equation of motion as: d2x/dt2 + ω02⋅x + (b⋅ω0/k)⋅dx/dt = 0 And now comes a step I don't really understand. Apparently from the equation of motion (but maybe not) follows: b/mR = 2⋅ω0 What? Where does that come from? Is it because the oscillation is critically damped? I saw (on wiki, again) that for the case of a critically damped system, b/(2√(mk)) = 1 which basically leads to the same result but without having to define ω0. Hopefully someone can help me understand that step, while I hope the previous calculations are correct. Thank you very much in advance. Julien.