Determine the corresponding time function f̈(t)f̈or each of...

Determine the corresponding time function \"f(t)\" for each of the following Laplace Transforms \"F(s):\" a) $F(s) = \frac{110}{s}$ b) $F(s) = \frac{1960}{s^2 + 196}$ c) $F(s) = \frac{56s}{s^2 + 196}$ d) $F(s) = \frac{40s + 20}{s^2 + 9s + 14}$ e) $F(s) = \frac{30s + 102}{s^2 + 4s + 40}$

Transcript

00:01 In this problem of laplace transform we have to find the laplace inverse for this given laplace so this is part a f s is equals to 10 plus s square plus 1 divided with s square plus 4 now here this term can be written as 10 plus 11 11 and 11 minus 3 divided with s square plus 4 because this term can be written as s square plus 1 s square plus 4 and this would be with minus 3 so this term is simply 11 minus 3 divide with s square plus 4 so we can write ft so 11 that means 11 and delta t minus this would be 3 divide with 2 that is 1 .5 so 1 .5 and this would be signed 4 can be written as 2 square so this would be 2 t now for part b we have given g s so g s is equals to e to the part minus s plus 4 e to the power minus 2 s divided with s square plus 6 s plus 8 now this term in the denominator can be written as say e to the power minus s plus 4 e to the power minus 2 s divided with this is s square plus 6 s plus 8 so this can be written as s plus 2 with s plus 4 and now we assume that this is the term say 1 divide with s plus 2 multiplied with s plus 4 from the partial fraction we can write it as a divided with s plus 2 plus b divided with so this is b divided with s plus 4 now we can write the value of a and b respectively so this would be written as say e to the power minus s so this is e to the power minus s divided with 2 and we have the value of a and b so this is 1 divide with s plus 2 plus 1 divide with s plus 4 and here this would be 4 multiplied with and then this would be 2 e to the power minus 2 s multiplied with the same term so 1 divide with s plus 2 plus 1 divide with s plus 4 now we have the simple values for this term so is to the power minus is divided with two that is half so this would be simply 0 .5 and e to the power minus 2 t minus 1 this would be power 1 is decreased and this would be minus e to the power minus 4 t to the t minus 1 so this is t minus 1 multiplied with u t minus 1 plus 2 multiplied with whole term so e to the power minus 2 is multiplied with t minus 2 minus e to the power minus 4 multiplied with t minus 2 is whole multiplied with u of t minus 2.

03:30 So this is we can say this is gt or we can say g inverse of s.

03:37 Now we have the answer for both part a and part b.

03:42 Respectively...

Question

Determine the corresponding time function \"f(t)\" for each of the following Laplace Transforms \"F(s):\" a) $F(s) = \frac{110}{s}$ b) $F(s) = \frac{1960}{s^2 + 196}$ c) $F(s) = \frac{56s}{s^2 + 196}$ d) $F(s) = \frac{40s + 20}{s^2 + 9s + 14}$ e) $F(s) = \frac{30s + 102}{s^2 + 4s + 40}$

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