Question
Download Solution PDFThe Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\). Then Laplace transform of e−6tx(t) is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct option is 1
Concept:
If the Laplace transform of a function \( x(t) \) is known, then the Laplace transform of \( e^{-at}x(t) \) can be obtained using the time-shifting property of the Laplace transform.
This property states that:
\( \mathcal{L}\{e^{-at}x(t)\} = X(s + a) \), where \( X(s) = \mathcal{L}\{x(t)\} \)
Given:
\( \mathcal{L}\{x(t)\} = \sqrt{\frac{2}{s - 3}} \)
Calculation:
We are asked to find the Laplace transform of \( e^{-6t}x(t) \).
Using the time-shifting property:
\( \mathcal{L}\{e^{-6t}x(t)\} = \sqrt{\frac{2}{(s + 6) - 3}} = \sqrt{\frac{2}{s + 3}} \)
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