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the output y are related by Consider a system L{f(t)} = y(t), for t20, where the input f and y"(t) + 3y' (t) + 2y(t) = f(t), y(0) = 0, y'(0) = 0. (a) Is the system linear? In symbols: if L{f} = y₁ and L{f2} = 92, and c is a constant, is it true that L{fi+cf2}= y1+ cy2? Justify. (b) Use the Laplace transform to find the output y(t) when the input is f(t) = cos(2t)-e-2t, t≥ 0.

the output y are related by Consider a system L{f(t)} = y(t), for t20, where the input f and y"(t) + 3y' (t) + 2y(t) = f(t), y(0) = 0, y'(0) = 0. (a) Is the system linear? In symbols: if L{f} = y₁ and L{f2} = 92, and c is a constant, is it true that L{fi+cf2}= y1+ cy2? Justify. (b) Use the Laplace transform to find the output y(t) when the input is f(t) = cos(2t)-e-2t, t≥ 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4. the output y are related by Consider a system L{f(t)} = y(t), for t20, where the input f and y"(t) + 3y' (t) + 2y(t) = f(t), y(0) = 0, y'(0) = 0. (a) Is the system linear? In symbols: if L{f} = y₁ and L{f2} = 92, and c is a constant, is it true. that L{fi + cf2} = y + cy2? Justify. (b) Use the Laplace transform to find the output y(t) when the input is f(t) = cos(2t) -e-2t, t≥ 0.
Transcribed Image Text:4. the output y are related by Consider a system L{f(t)} = y(t), for t20, where the input f and y"(t) + 3y' (t) + 2y(t) = f(t), y(0) = 0, y'(0) = 0. (a) Is the system linear? In symbols: if L{f} = y₁ and L{f2} = 92, and c is a constant, is it true. that L{fi + cf2} = y + cy2? Justify. (b) Use the Laplace transform to find the output y(t) when the input is f(t) = cos(2t) -e-2t, t≥ 0.
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