Question

Part I: For each problem, there is only one right answer 1. The model of a system in the frequency domain is A. the transfer function from the input to the output. B. the differential equation which defines the relation between the input and the output. C. the zero-state response of the system D. None 2. For a system whose input r and output y are related by the differential equation u(0)a30) dr(t) +3r(t) dt dt2 the transfer function from input r to output y is A. 32 C. (s2+3s2)(s +2) D. None +3s+2 3. For a negative unity feedback system, R(s) E(s) C(s) G(s) where G(s) s2 5s6 3.1. the zeros of the closed-loop system are_ A. 2, 3 B.-2, -3; C.2; D. -2. -4; E. None 3.2. the poles of the closed-loop system are A. 2,3 B.2,-3; C.-1; D. -2,-4; E. None 4. A system has the following transfer function H(s) This sysem is A. an underdamped system B. an overdampled system C. a critically damped system D an undamped system E. None 5. For an underdamped system, the RIGHT statement is_. A. the damping ratio of the system is greater than one B. the damping ratio of the system is smaller than one and is larger than zero C. the damping ratio is one. D. None

Answer 1

The model of the system in frequency domain is the transfer function between input to the output H (s) = y (s)/x (s) therefore option ' A ' is correct d^2 y (t)/ d + 2 + 3 dy (t)/dt + 2y (t) = dx (t)/dt + 3 x (t) t y (t) rightarrow output x (t) rightarrow Input Take Laplace transform s^2 y (s) + 3s y (s) + 2 (s) = sx (s) + 3 x (s) rightarrow y (s)/x (s) = s + 3/s^2 + 3s + 2 option ' B ' is correct therefore G (s) = s + 2/s^2 + 5s + 6 H