Question

Find the inverse Laplace transform by convolution integral. Show the details of your work. 1. $F(s) = \frac{5.5}{(s+1.5)(s-4)}$ 2. $F(s) = \frac{2\pi s}{(s^2+w^2)^2}$ 3. $F(s) = \frac{2}{(s^2+w^2)s^2}$

Name: find the inverse laplace transform by convolution integral show the details of your work 1 fs frac55s15s 4 2 fs frac2pi ss2w22 3 fs frac2s2w2s2 54777
Uploaded: 2024-08-01T12:21:06-08:00
Duration: 1 min 40 s
Channel: Adi S
Description: find the inverse laplace transform by convolution integral show the details of your work 1 fs frac55s15s 4 2 fs frac2pi ss2w22 3 fs frac2s2w2s2 54777

          Find the inverse Laplace transform by convolution integral. Show the details of your work.
1. $F(s) = \frac{5.5}{(s+1.5)(s-4)}$
2. $F(s) = \frac{2\pi s}{(s^2+w^2)^2}$
3. $F(s) = \frac{2}{(s^2+w^2)s^2}$

$find the inverse laplace transform by convolution integral show the details of your work 1 fs frac55s15s 4 2 fs frac2pi ss2w22 3 fs frac2s2w2s2 54777$

Added by Ashley W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

08/01/2024

Step 1

$F(s) = \frac{5.5}{(s+1.5)(s-4)}$ Let $F(s) = G(s)H(s)$, where $G(s) = \frac{1}{s+1.5}$ and $H(s) = \frac{5.5}{s-4}$. Then $g(t) = e^{-1.5t}$ and $h(t) = 5.5e^{4t}$. The convolution integral is given by $f(t) = \int_0^t g(\tau)h(t-\tau) d\tau = \int_0^t Show more…

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Find the inverse Laplace transform by convolution integral. Show the details of your work. 1. $F(s) = \frac{5.5}{(s+1.5)(s-4)}$ 2. $F(s) = \frac{2\pi s}{(s^2+w^2)^2}$ 3. $F(s) = \frac{2}{(s^2+w^2)s^2}$