Solution_to_problem_3.5

# Solution_to_problem_3.5 - The Laplace transform of the...

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3.5 – 1 Solution to problem 3.5 Before writing T(s), we first need to write down an expression for T(t). To this purpose we need to decompose the temperature profile. The temperature profile can be written as: ( ) ( ) ( ) ( ) ( ) 30 30 30 55 30 55 20 - - - + = t S t t S t t S t T In the above equation S(t) represents the unit step function, and S(t-30) represents the unit step function delayed by 30 minutes.
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Unformatted text preview: The Laplace transform of the above equation can now be taken (see Table 3.1, page 54 in the textbook): ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) s s e s s e s s s t S t t S t t S L t T L s T ⋅-⋅--⋅ + = ⋅ ⋅-⋅ + = -⋅--⋅ + ⋅ = = 30 2 30 2 2 1 1 30 55 20 1 30 55 1 30 55 20 30 30 30 55 30 55 20...
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