Consider the mass-spring-damper system with the transfer function g(s) = x(s) f(s) = 1 ms2 + cs + k where x(s) and f(s) denote respectively the laplace transforms of displacement of mass and input force, m = 1 kg, c is damping constant, and k is the stiffness.

(a) we would like to study the bode diagram of this system for a damping ratio of 5 = 0.05 and natural frequency of wn = 10 rad/sec. select cand k under these and wn settings, and next plot the bode diagram of the system for the selected c and k values using matlab bode command.
(b) reading the bode diagram, answer the following: (i) if the input force is in the form sin(t), i. e., the excitation frequency is w = 1 rad/sec, what is m and o for the output z(t) = m sin(t + o). (ii) if the input force is in the form sin(10t), what is m and o for the output z(t) = m sin(10t + º). (iii) if the input force is in the form sin(100t), what is m and 6 for the output c(t) = m sin(100t + ).
(c) validate step (b) using time simulations in simulink.