3s2 + 8s + 9 1-J = (1)f (8) (s + 2)³

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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 \( y(t) \).
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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