Unit-2

Laplace Transformation

Question Bank

Question-1: Find the Laplace transform of (1 + cos 2t)

Sol.

So that-

Question-2: Find the Laplace transform of t sin at.

Sol. Here-

Question-3: Find the Laplace transform of

Sol. Here-

So that-

As we know that-  

So that-

Hence-

Question-4: Find-

Given that,

Sol.

By using change of scale property-

Question-5: Express the function given below in terms of unit step function and find its Laplace transform as well-

Sol. Here we are given-

So that-

Question-6: Find the Laplace transform of the following function by using unit step function-

Sol.

Since

Question-7: Find the Laplace transform of

Where-

Sol. Here we are given—

As

Question-8: Apply convolution theorem to evaluate-

Sol.

Since

By convolution theorem, we get-

Because- f(u) = cos au, g(t-u) = cos b(t – u)

Question-9: Find the inverse Laplace transform of-

Sol.

Question-10: Find

Sol.

Question-11: Find the inverse transform of-

Sol.

First we will convert it into partial fractions-

Question-12: Use Laplace transform method to solve the following equation-

Sol. Here we have-

Take Laplace transform of both sides, we get-

It becomes-

                         (

So that-

Now breaking it into partial fractions-

We get the following results on inversion-