Quick Reference: Use Partial Fraction Decomposition (PFD) to break complex \(F(s)\) into forms matching basic table entries like \(\frac{a}{s^2+a^2}\) or \(\frac{s-a}{(s-a)^2+b^2}\).
Exercises: Find \(f(t) = \mathcal{L}^{-1}\{F(s)\}\)
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(a) \(F(s)= \frac{\sqrt{2}}{s^2-9}\)
(b) \(F(s)= \frac{3s}{s^2+4}\)
Video Solution
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(a) \(F(s)= \frac{1}{s^2-4s+5}\)
(b) \(F(s)= \frac{2s}{s^2-s-6}\)
Video Solution
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(a) \( F(s)=\frac{s^3}{s^4-1}\)
(b) \(F(s)=\frac{s^3+s^2}{s^4-1}\)
(c) \( F(s)=\frac{s^3+s}{s^4-1} \)
Video Solution
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\(H(s)=\left(\frac{2}{s}+\frac{1}{s^2}\right)+e^{-s}\left(\frac{3}{s}-\frac{1}{s^2}\right)+e^{-3 s}\left(\frac{1}{s}+\frac{1}{s^2}\right)\)
Video Solution
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\(F(s)= \frac{1}{s(s+1)}\) (using Convolution integral)
Video Solution