Test: Laplace Transform- 2 - Electronics and Communication Engineering (ECE) MCQ

Step 1: Start with the given expression for G(s)

The expression is:

We are tasked with finding its inverse Laplace transform.

Step 2: Complete the square in the denominator

To simplify, complete the square in the denominator of G(s):

Step 3: Split the expression into two parts

Now, the next step is to express the numerator in a way that will be easier to handle with known inverse Laplace transform formulas. We can break the numerator s as:

Step 4: Apply the inverse Laplace transform

Now, apply the inverse Laplace transform to each term separately.

• The first term  corresponds to the inverse Laplace transform of 

• The second term  corresponds to the inverse Laplace transform of 

Thus, we have:

A second-order differential equation is represented as:
y" + ay' + by = f(t)
The Laplace transform of the above equation with the initial condition is:
s²Y(s) - sY(0) - Y'(0) + a[sY(s) - Y(0)] + bY(s) = F(s)

Calculation
Given, y(0) = 5, y'(0) = 10
S²Y(s) - 5s - 10 + a (sY(s) - 5) + bY(s) = F(s)
Hence, the correct answer is option 2.