3s2 + 8s + 9 1-J = (1)f (8) (s + 2)³
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Author:Erwin Kreyszig
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Can you help me with question 3a?
![## Inverse Laplace Transforms
This section involves determining the inverse Laplace transforms of given functions.
### Problem 2: Determine the inverse Laplace transforms.
**(a)**
\[
f(t) = \mathcal{L}^{-1} \left\{ \frac{3}{s} \right\}
\]
**(b)**
\[
g(t) = \mathcal{L}^{-1} \left\{ \frac{-3s + 4}{s^2 + 9} \right\}
\]
**(c)**
\[
h(t) = \mathcal{L}^{-1} \left\{ \frac{-3s + 4}{s^2 + 4s + 20} \right\}
\]
### Problem 3: Determine the inverse Laplace transforms.
**(a)**
\[
f(t) = \mathcal{L}^{-1} \left\{ \frac{3s^2 + 8s + 9}{(s + 2)^3} \right\}
\]
**(b)**
\[
y(t) = \mathcal{L}^{-1} \left\{ \frac{s^2 + 11s + 20}{(s^2 + 4s + 8)(s + 1)^2} \right\}
\]
Follow the guidelines provided in this section to solve these inverse Laplace transforms for each function \( f(t) \), \( g(t) \), \( h(t) \), and \( y(t) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3143ece0-b2b2-417b-825f-ab4e468fd03e%2Fce2c0908-2ccc-4148-aa84-84e499211e84%2Fo20vk1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Inverse Laplace Transforms
This section involves determining the inverse Laplace transforms of given functions.
### Problem 2: Determine the inverse Laplace transforms.
**(a)**
\[
f(t) = \mathcal{L}^{-1} \left\{ \frac{3}{s} \right\}
\]
**(b)**
\[
g(t) = \mathcal{L}^{-1} \left\{ \frac{-3s + 4}{s^2 + 9} \right\}
\]
**(c)**
\[
h(t) = \mathcal{L}^{-1} \left\{ \frac{-3s + 4}{s^2 + 4s + 20} \right\}
\]
### Problem 3: Determine the inverse Laplace transforms.
**(a)**
\[
f(t) = \mathcal{L}^{-1} \left\{ \frac{3s^2 + 8s + 9}{(s + 2)^3} \right\}
\]
**(b)**
\[
y(t) = \mathcal{L}^{-1} \left\{ \frac{s^2 + 11s + 20}{(s^2 + 4s + 8)(s + 1)^2} \right\}
\]
Follow the guidelines provided in this section to solve these inverse Laplace transforms for each function \( f(t) \), \( g(t) \), \( h(t) \), and \( y(t) \).
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