3. A system can be described by the differential equation ° +3y+2y =1+1 with initial conditions y(0) = 0 and y(0)=1. (a)

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3 A System Can Be Described By The Differential Equation 3y 2y 1 1 With Initial Conditions Y 0 0 And Y 0 1 A 1 (88.91 KiB) Viewed 22 times

3. A system can be described by the differential equation ° +3y+2y =1+1 with initial conditions y(0) = 0 and y(0)=1. (a) Find the total response of the system. (b) Find the free response of the system. (c) Find the forced response of the system. (d) Find the transient response of the system. (e) Find the steady state response of the system. + s#+9s +19 4. For the system's transfer function G(s= (s +1)(8 + 2)(s+4) (a) What are the system's poles and zeros? (b) Find the unit impulse response of the system? (c) Is this system stable or unstable? Why? 5. The unit impulse responses of several systems are given below. For each case determine if the impulse response represents a stable or an unstable system. (a) h(t)=e" (b) h(t)= te' (c) h(t)=1 (d) h(t)=esin 31
(e) h(t)=sin or