Determine the Laplace transform of the given function f. f(t)=(t -1)^2 u_2(t)

Determine the Laplace transform of the given function f. f(t)=(t -1)^2 u_2(t)

Question
Laplace transform
asked 2021-03-07
Determine the Laplace transform of the given function f.
\(f(t)=(t -1)^2 u_2(t)\)

Answers (1)

2021-03-08
Step 1
Here laplace transform of given function is to be calculated.
Given function is \(f(t)=(t -1)^2 u_2(t)\)
So expand the function as follows,
\(f(t)=t^2u(t)+u(t)-2tu(t)\)
Take Laplace of the function f(t)
Step 2
Then,
\(L(f(t))=L(t^2u(t)+u(t)-2tu(t))\)
\(=\frac{2}{s^3}+\frac{1}{s}-\frac{2}{s^2}\)
Hence the Laplace Transform of the \(f(t)=(t-1)^2u(t) \text{ is } \frac{2}{s^3}+\frac{1}{s}-\frac{2}{s^2}\)
0

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