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H9P3: DESIGNING A SHOCK ABSORBER
1. Assume s=y(t) - Yroad(t), so differential eqn becomes ms^2+bs+k=0. Dividing by m, s^2+(b/m)s+k/m=0 Compare this to s^2+2as+w0^2 so, a=b/(2m) 2. From above eqn, similarly, w0 = sqrt(k/m) 3. frequency = w0/(2*pi) = sqrt(k/m)/(2*pi) 4. If you critically damp, then sqrt((2a)^2-4(w0)) = 0 sqrt((b/m)^2 - 4k/m) = 0 solving, b = 2sqrt(km)