Question

H9P3: DESIGNING A SHOCK ABSORBER

Answer 1

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)