Question:medium
Find the inverse transform of
\[
F(S)=\frac{S^2+3}{(S^2+25+5)(S+2)}
\]
Find the inverse transform of
\[
F(S)=\frac{S^2+3}{(S^2+25+5)(S+2)}
\]
Show Hint
For inverse Laplace transforms:
• Complete the square in quadratic terms.
• Use partial fractions.
• Match with standard sine and cosine transform forms.
• Complete the square in quadratic terms.
• Use partial fractions.
• Match with standard sine and cosine transform forms.
Updated On: May 22, 2026
- \(\dfrac{7}{5}e^{-2t}-\dfrac{2}{\sqrt{5}}e^{-t}\cos\left(2t-\tan^{-1}2\right)\)
- \(\dfrac{7}{5}e^{-2t}+\dfrac{2}{\sqrt{5}}e^{-t}\cos\left(2t-\tan^{-1}2\right)\)
- \(\dfrac{7}{5}e^{-2t}+\dfrac{2}{\sqrt{5}}e^{-t}\sin\left(2t-\tan^{-1}2\right)\)
- \(\dfrac{7}{5}e^{-2t}-\dfrac{2}{\sqrt{5}}e^{-t}\sin\left(2t-\tan^{-1}2\right)\)
Show Solution
The Correct Option is B
Solution and Explanation
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