Solution_to_problem_3.4 - r r r r r r t t S t t a t t S t t...

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3.4 – 1 Solution to problem 3.4 a) Before writing F(s), we first need to write down an expression for f(t). To this purpose we need to decompose the function. The function can be written as: ( ) ( ) ( ) ( ) 6 1 2 4 5 - - - - = t S t S t S t f In the above equation S(t) represents the unit step function, and S(t-2) and S(t-6) represent the unit step function delayed by 2 and 6 minutes respectively. The Laplace transform of the above equation can now be taken (see Table 3.1, page 54 in the textbook): ( ) ( ) ( ) ( ) ( ) ( ) ( ) s s e s e s s t S t S t S L t f L s F - - - - = - - - - = = 6 2 1 4 5 6 2 4 5 b) a) Before writing F(s), we first need to write down an expression for f(t). To this purpose we need to decompose the function. The function can be written as:
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Unformatted text preview: ( ) ( ) ( ) ( ) ( ) ( ) ( ) r r r r r r t t S t t a t t S t t a t t S t t a t a t f ⋅-⋅ ⋅-+ ⋅-⋅ ⋅---⋅--⋅ = 3 3 2 2 The Laplace transform of the above equation can now be taken (see Table 3.1, page 54 in the textbook): ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) s t s t s t s t s t s t r r r r r r r r r r r r e e e s a e s a e s a e s a s a t t S t t a t t S t t a t t S t t a t a L t f L s F ⋅ ⋅-⋅ ⋅-⋅-⋅ ⋅-⋅ ⋅-⋅-+--= ⋅ + ⋅-⋅-= ⋅-⋅ ⋅-+ ⋅-⋅ ⋅---⋅--⋅ = = 3 2 2 3 2 2 2 2 2 1 3 3 2 2...
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