A spring-mass-damper system, is used as a shock absorber for a large high-performance motorcycle. The original parameters selected are m = 1 kg, b = 9 N s/m. and k = 20 N/m.
(a) Determine the system matrix, the characteristic roots, and the transition matrix Φ(t). The harsh initial conditions are assumed to be y(0) = 1 and dy/dt|t=0 = 2.
(b) Plot the response of y(t) and dy/dt for the first two seconds.
(c) Redesign the shock absorber by changing the spring constant and the damping constant in order to reduce the effect of a high rate of acceleration force d2y/dt2 on the rider. The mass must remain constant at l kg.