b. C. C(s) R (s) C(s) R(s) X(s) F(s) = = 5s + 2 s² + 4s +3 2s³ + 1 s² +8s +6 S4 - s² +8s +3 S5 + 5s4 - 2s3 + 7s² +1' -, assume r(t) = 6t4

2) Consider the spring-mass-damper system hanging down from a ceiling. Initially, the system is at rest. Then, we gently place another mass (M) on top the original one (m). First, please obtain the equation of motion of the mass m in the system (before we placed the other object). Assign the displacement references yourself and obtain the equation accordingly. From the equation of motion, please obtain the transfer function, G(s), between an external force on the mass m , f(t), and the displacement of the mass m, x(t). Then, please obtain the motion of the object M, using the transfer function G(s). Don't forget that G(s) belongs to the system shown on the top! To solve this, represent the force applied by the added mass (M) as a function of time. How would you describe the act of adding a mass as an external force input? Then solve for x(t). c = 10 Ns/m k = 50 N/m m = 5 kg M M = 25 kg F(s) G(s) X(s)

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