4. This is a typical exam question. Consider a system L{f(t)} = y(t), for t 20,...

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4. This is a typical exam question. Consider a system L{f(t)} = y(t), for t 20, where the input f and the output y are related by 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 e 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. 4. This is a typical exam question. Consider a system L{f(t)} = y(t), for t 20, where the input f and the output y are related by 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 e 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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a To determine if the system is linear we need to check if it satisfies the properties of linearity ... View the full answer