Consider the 1" -order continuous-time (CT) LTI dynamical system given by the input-output differential equation dy(t) = -3y(t) + x(t) dt y(0-) =0. Let the following symbols be used: and the state Yın1): impulse response Yzıa (1): zero-input response Yzsa (1): zero-state response Yea(1): complete response Yese () : unit-step response Yus (1): homogeneous solution Ys(1): particular solution Let x(1) = 8(1), the Dirac's delta signal. Fill in the blanks in Table 1. Let x(1) = u(1), the unit-step signal. Fill in the blanks in Table 2. а) b)

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Consider the 1* -order continuous-time (CT) LTI dynamical system given
by the input-output differential equation
dy(t)
= -3y(t) + x(t)
dt
y(0-) =0.
Let the following symbols be used:
and the state
Y'm(0): impulse response
Yzın (t): zero-input response
Vzsa (1): zero-state response
Yea (1): complete response
Yesa () : unit-step response
Yus (1): homogeneous solution
Ys 1): particular solution
Let x(1) = 8(1), the Dirac's delta signal. Fill in the blanks in Table 1.
Let x(t) = u(t), the unit-step signal. Fill in the blanks in Table 2.
Now change the input and the state in the above dynamical system and
a)
b)
c)
let
dy(t)
= -3y(t) – 28(t) + 3u(t)
dt
y(0") = -5.
Fill in the blanks in Table 3.
Table 1
Yzz(1)
Yzz (1)
Ycr(1)
Table 2
Yese (1)
Yzz(1)
Table 3
Yz (1)
Ys (1)
Transcribed Image Text:Consider the 1* -order continuous-time (CT) LTI dynamical system given by the input-output differential equation dy(t) = -3y(t) + x(t) dt y(0-) =0. Let the following symbols be used: and the state Y'm(0): impulse response Yzın (t): zero-input response Vzsa (1): zero-state response Yea (1): complete response Yesa () : unit-step response Yus (1): homogeneous solution Ys 1): particular solution Let x(1) = 8(1), the Dirac's delta signal. Fill in the blanks in Table 1. Let x(t) = u(t), the unit-step signal. Fill in the blanks in Table 2. Now change the input and the state in the above dynamical system and a) b) c) let dy(t) = -3y(t) – 28(t) + 3u(t) dt y(0") = -5. Fill in the blanks in Table 3. Table 1 Yzz(1) Yzz (1) Ycr(1) Table 2 Yese (1) Yzz(1) Table 3 Yz (1) Ys (1)
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