Question

A linear, time-invariant system is modeled by the ordinary differential equation

y(t) + 7y(t) = 14f(t)

Let f(t) = e^-t cos(2t)u(t) and y(0-) = -1.

(a) Find the transfer function of the system and place your answer in the standard form

H(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 + ... + a1s + a0

(b) Determine the output of the system as

Y(s) = Yzs(s) + Yzi(s)

and place both the zero state and the zero input solutions into the standard form:

Yzs(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 + ... + a1s + a0

&

Yzi(s) = bms^m + bm-1s^m-1 + ... + b1s + bo / s^n + an-1s^n-1 + ... + a1s + a0

2. (12 points) A linear, time-invariant system is modeled by the ordinary differential equation y(t)7y(t) 14f (t) Let f(t) = e-t cos(2t)u(t) and y(0-) = -1. (a) (3 points) Find the transfer function of the system and place your answer in the standard form bmsmbm-1sm-1. b1s+b S an-1s-1 +... + a1s +ao ... H(s) = (b) (9 points)Determine the output of the system as Y (s) = Y2 (s) + Yzi(s) and place both the zero state and the zero input solutions into the standard form: bm smbm-1 sm-1+.+b1s +bo Sn an-1sn-1 +... + a1 8 ao bmsm bm-1 Sm-1 +... + b1s+ b & Yzi(s) = Yas (s) = sn an-18n- ..+a18 + ao

Answer 1

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