Question

. (40pts) Consider a spring-mass-damper system shown below, where the input u() is displacement input at the right end of the spring k3 and x() is the displacement of mass ml. (Note that the input is displacement, NOT force) k3 k1 m2 (a) (10pts) Draw necessary free-body diagrams, and the governing equations of motion of the system. (b) (10pts) Find the transfer function from the input u() to the output x(t). (c) (10pts) Given the system parameter values of m1-m2-1, cl-c2-2, ki-k21, k3-2, show that the system transfer function can be found as 2(s +2) X (s) U(s) s +6s3 +9s +12s +5 (d) (10pts) Find the response x) when u(b) is a unit step input and identify the steady-state and the transient part of the response. What is the steady-state value of the response? Note that you must identify the exponents of all exponential functions and the frequencies of all trigonometric function, but you don't need to caleulate the coefficients of the functions or phase angles.

Answer 1

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