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Q5) Compute the output y(t) of the systems below. In all cases, consider the system with zero initial conditions. TIP: use the convolution table and remember the properties of convolution. a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)

Q5) Compute the output y(t) of the systems below. In all cases, consider the system with zero initial conditions. TIP: use the convolution table and remember the properties of convolution. a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Q5) Compute the output y(t) of the systems below. In all cases, consider the system with zero initial conditions. TIP: use the convolution table and remember the properties of convolution. a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) b) h(t) = 28(t)- 4 exp(-3t) u(t) and input x(t) = 3 u(t) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)
Transcribed Image Text:Q5) Compute the output y(t) of the systems below. In all cases, consider the system with zero initial conditions. TIP: use the convolution table and remember the properties of convolution. a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) b) h(t) = 28(t)- 4 exp(-3t) u(t) and input x(t) = 3 u(t) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t)
Q5.) a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) conv(x(t),h(t)) = 6*t*exp(-2*t)*u(t) B conv(x(t).h(t)) = t*exp(-t)*u(t) conv(x(t).h(t)) = 2*t*exp(-t)*u(t) conv(x(t),h(t)) = 5*exp(-2*t)*u(t) Q5.) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t) A conv(x(t),h(t)) = u(t) + 2*(1-exp(-3*t))*u(t) B conv(x(t).h(t)) = 7*u(t) +9*(1-exp(-3*t))*u(t) conv(x(t),h(t)) = 4*u(t)-(1-exp(-3*t))*u(t) conv(x(t),h(t)) = 6*u(t) - 4*(1-exp(-3*t))*u(t) Q5.) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t) conv(x(t).h(t)) = 6*[0.1*exp(-3*t) - 0.6*exp(-2*t) *cos(3*t+71.56°)]* u(t) B conv(x(t).h(t)) = [0.2*exp(-t) - 0.125*exp(-2*t)*cos(3*t+71.56°)]*u(t) conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-2*t)* cos(3*t+71.56°)]*u(t) conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-t)*sin(3*t+71.56°)]*u(t)
Transcribed Image Text:Q5.) a) h(t) = 3 exp(-2t) u(t) and input x(t) = 2 exp(-2t) u(t) conv(x(t),h(t)) = 6*t*exp(-2*t)*u(t) B conv(x(t).h(t)) = t*exp(-t)*u(t) conv(x(t).h(t)) = 2*t*exp(-t)*u(t) conv(x(t),h(t)) = 5*exp(-2*t)*u(t) Q5.) b) h(t) = 28(t)-4 exp(-3t) u(t) and input x(t) = 3 u(t) A conv(x(t),h(t)) = u(t) + 2*(1-exp(-3*t))*u(t) B conv(x(t).h(t)) = 7*u(t) +9*(1-exp(-3*t))*u(t) conv(x(t),h(t)) = 4*u(t)-(1-exp(-3*t))*u(t) conv(x(t),h(t)) = 6*u(t) - 4*(1-exp(-3*t))*u(t) Q5.) c) h(t) = 2 exp(-t) u(t) and input x(t) = 4 exp(-2t) cos(3t) u(t) conv(x(t).h(t)) = 6*[0.1*exp(-3*t) - 0.6*exp(-2*t) *cos(3*t+71.56°)]* u(t) B conv(x(t).h(t)) = [0.2*exp(-t) - 0.125*exp(-2*t)*cos(3*t+71.56°)]*u(t) conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-2*t)* cos(3*t+71.56°)]*u(t) conv(x(t).h(t)) = 8*[0.1*exp(-t) - 0.316*exp(-t)*sin(3*t+71.56°)]*u(t)
Expert Solution
Step 1

Given:

1. h(t) = 3e-2tu(t) & x(t)= 2e-2tu(t)2. h(t) = 2δ(t)-4e-3tu(t) & x(t)=3u(t)3. h(t) = 2e-tu(t) & x(t)= 4e-2tcos(3t)u(t)

Find:

Output of system using convolution property ?

 

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