# Question 2.7.5: Four Repeated Roots Choose the most convenient method for ob...

Four Repeated Roots

Choose the most convenient method for obtaining the inverse transform of

$X(s)=\frac{s^2+2}{s^4(s+1)}$

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.
The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.

Question: 2.1.6

## Find the complete response of the following equation. ẍ + 4ẋ + 53x = 15us(t) x(0) = 8 ẋ (0) = −19 ...

We cannot use Table 2.1.1 for this part because th...
Question: 2.9.2

Question: 2.9.1

Question: 2.9.3

Question: 2.3.3

## The Sine and Cosine Functions Derive the Laplace transforms of the exponentially decaying sine and cosine functions, e ^−at sin𝜔t and e ^−at cos𝜔t, for t ≥ 0, where a and 𝜔 are constants. ...

Note that from the Euler identity, e^{j\the...
Question: 2.7.7

## Two Complex Roots Use two methods to obtain the inverse Laplace transform of X(s) = 3s + 7/4s² + 24s + 136 = 3s + 7/4(s² + 6s + 34) ...

a. The denominator roots are s = −3 ± 5j. To avoid...
Question: 2.7.4

## Exponential Response of a First-Order Model Use the Laplace transform to solve the following problem. ẋ + 5x = 7te ^−3t x(0) = 0 ...

Taking the transform of both sides of the equation...
Question: 2.7.2

## One Negative Root and Two Zero Roots The inverse Laplace transform of X(s) = 5/s²(3s + 12) ...

The denominator roots are s= −12/3= −4, s=0, and s...
Question: 2.7.1

## A Third-Order Equation Obtain the solution of the following problem: 10 d³x /dt³ + 100 d²x /dt² + 310 dx /dt + 300x = 750us(t) x(0) = 2 ẋ(0) = 4 ẍ(0) = 3 ...

Because f(t) = 𝛿(t), F(s) = 1, and X(s)=\fr...