You have the following mechanical parts at your disposal. 2 Springs with stiffne

Question

You have the following mechanical parts at your disposal.
2 Springs with stiffness k1 = 10000 N/m
2 Springs with stiffness k2 = 3000 N/m
2 Masses with mass m1 = 4 kg 2 masses with mass m2 = 10 kg
1 damper with damping c = 200 N s/m
You can create systems using these components on a horizontal surface without friction. You may connect a spring or a damper to a wall.

Using these parts, design the following...
1. a second order system with the smallest settling time
2. a second order system with the smallest percent overshoot
3. a system that has a zero steady state output in response to the input f(t) = 100cos(70.71t)

Explanation / Answer

1. Settling Time is 4/(tau*w) = 4M/c For smallest settling time maximise M and minimise c M=28kg and c=200N/m 2.Smallest percent overshoot = Highest tau = c/k c=200N/m and k=k2=3000 series with 10000 = 2600N/m 3.lim s->0 for sG(s) =0 For any system of type 0 or 1 this will be valid Cheers! Good luck!

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