Answer Happy

Problem-4. The translational system given has the following mass, friction and spring values: M = 2kg, f₂ = 4N-s/m and K = 8N/m, K (a) Write the equation of motion (as a differential equation). 0000 M (b) Represent the system in state-space (where the states are x₁ = x (displacement in m) and x₂ = v (velocity in m/s), the input u is force f and the output y is the displacement (x) (c) Write the transfer function of G₁ (s) = X(s)/F(s). fv (d) Write the transfer function of G₂(s) = V(s)/F(s). (e) Plot the step response of displacement vs. time. (f) What would be the output x (t) in meters in steady-state when the applied input is f(t) = 2 N. (g) What would be the peak value of output x (t) in meters when the applied input is f(t) = 2 N. (h) Plot the step response of velocity vs. time. (i) What would be the output v(t) in meters per sec in steady-state when the applied input is f(t) = 2 N. (j) What would be the peak value of output v(t) in meters per sec when the applied input is f (t) = 2 N. C x(1) f(t)