# Question please answer all the questions and sub questions For the following Laplace domain functions, determine the equivalent time domain functions: a) F(s) = 10 / (s(s+1)(s+10)) b) F(s) = 2(5+2)/((s+1)(s2 + 4)) Solve the following ODEs using Laplace Transforms: a) y(t) – 2y(t) + 4y(t) = 0 ... Initial conditions: y(0) = 1, y(t) = 2 b) y(t) + 2y(t)= el Initial conditions:y(0) = 1, y(t) = 2

EYLCST The Asker · Mechanical Engineering
please answer all the questions and sub questions

Transcribed Image Text: For the following Laplace domain functions, determine the equivalent time domain functions: a) F(s) = 10 / (s(s+1)(s+10)) b) F(s) = 2(5+2)/((s+1)(s2 + 4)) Solve the following ODEs using Laplace Transforms: a) y(t) – 2y(t) + 4y(t) = 0 ... Initial conditions: y(0) = 1, y(t) = 2 b) y(t) + 2y(t)= el Initial conditions:y(0) = 1, y(t) = 2
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Transcribed Image Text: For the following Laplace domain functions, determine the equivalent time domain functions: a) F(s) = 10 / (s(s+1)(s+10)) b) F(s) = 2(5+2)/((s+1)(s2 + 4)) Solve the following ODEs using Laplace Transforms: a) y(t) – 2y(t) + 4y(t) = 0 ... Initial conditions: y(0) = 1, y(t) = 2 b) y(t) + 2y(t)= el Initial conditions:y(0) = 1, y(t) = 2
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Q(a) y^(¨)(t)-2y^(˙)(t)+4y(t)=0quad Given y(0)=1quady^(˙)(t)=2 quad take loplce taryform [s^(2)Y(s)-sY(0)-Y^(')(0)]-2[sY(s)-Y(0)]+4Y(s)=0 (s^(2)-2s+4)Y(s)=s(1)+(2)-2(1) (s^(2)-2s+4)Y(s)=s Y(s)=(s)/((s^(2)-2s+4))=(s)/([(s-1)^(2)+(sqrt3)^(2)])=>((s-1+1))/([s-1)^(2)+(sqrt3)^(2)]) Y(s)=((s-1))/([(s-1)^(2)+(sqrt3)^(2)])+(sqrt3)/(sqrt3[(s-1)^ ... See the full answer