Problem 2 based on Inverse Laplace Transform using Convolution Theorem | Summary and Q&A

TL;DR

This video tutorial explains how to find the inverse Laplace transform of a given function using the convolution theorem.

Key Insights

• 🔨 The convolution theorem is a useful tool for finding the inverse Laplace transform of a function.
• ❓ The partial fraction method is an alternative approach to finding the inverse Laplace transform.
• 🆘 Following a step-by-step process helps in solving the problem efficiently.
• ❓ The convolution theorem involves splitting the function, finding the inverse Laplace transform of each part, replacing variables, and integrating the product of the two transformed functions.
• 🤱 The d factorization formula for cos a * sin b is 2 * cos (a - b).

Transcript

hello friends so after covering the numerical on convolution theorem let's move ahead with the second numerical on convolution theorem so here i have one function of s which is different than the previous function and let's see how to find the inverse laplace of that by using convolutional theorem so let's start so here we have to find out inverse ... Read More

Questions & Answers

Q: What is the convolution theorem used for?

The convolution theorem is used to find the inverse Laplace transform of a function by splitting it into two parts and performing integration.

Q: Can we use other methods besides the convolution theorem?

Yes, other methods like partial fraction decomposition can also be used to find the inverse Laplace transform of a function. However, the convolution theorem is recommended for its simplicity.

Q: Why is it important to follow the steps in the video to find the inverse Laplace transform?

Following the steps ensures a systematic approach to solving the problem and simplifying the calculations. It also helps in understanding the concept of convolution theorem.

Q: How is the convolution theorem applied in finding the inverse Laplace transform?

The convolution theorem involves integrating the product of the inverse Laplace transforms of the two functions obtained from splitting the original function.

Summary & Key Takeaways

• The video tutorial demonstrates how to find the inverse Laplace transform of a function using the convolution theorem.

• The function to be transformed is s / ((s^2 + a^2)(s^2 + b^2)).

• The steps involved include splitting the function into two parts, finding the inverse Laplace transform of each part, replacing variables, and applying the convolution theorem.