Problem 2 Based on Inverse Laplace Transform using Shifting theorem - Engineering Mathematics 3 | Summary and Q&A

TL;DR

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

Key Insights

• 😀 The last term of a quadratic equation is crucial in converting a function of s into a function of s + a.
• 🤝 The shifting theorem simplifies the process of finding the inverse Laplace transform when dealing with functions of s + a.
• 🗂️ Dividing the numerator separately with the denominator helps obtain the final inverse Laplace transform.
• 😃 The formula for the inverse Laplace transform of 1/(s^2 - 2^2) is 1/(2sinh(2t)).
• 🎮 The video emphasizes the importance of understanding the shifting theorem and the Laplace transform to solve such numerical problems.
• 🎮 The video emphasizes the need to revise the formula for the inverse Laplace transform and watch related videos for a better understanding.

Transcript

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Questions & Answers

Q: What is the purpose of finding the last term of a quadratic equation when converting a function of s into a function of s + a?

Finding the last term helps convert the quadratic equation into a perfect square, making it easier to manipulate and find the inverse Laplace transform.

Q: How is the shifting theorem used in finding the inverse Laplace transform?

The shifting theorem states that the inverse Laplace transform of a function of s + a is equal to e^(-at) times the inverse Laplace transform of the function of s.

Q: Why is it necessary to divide the numerator separately with the denominator in the final step?

Dividing the numerator separately with the denominator allows the function to be simplified further and obtain the final inverse Laplace transform.

Q: What is the formula for finding the inverse Laplace transform of 1/(s^2 - 2^2)?

The formula for the inverse Laplace transform of 1/(s^2 - 2^2) is 1/(2sinh(2t)).

Summary & Key Takeaways

• The video discusses how to convert a function of s into a function of s + a by finding the last term of a quadratic equation.

• The shifting theorem is used to find the inverse Laplace transform of the function after converting it to a function of s - a.

• The final step involves dividing the numerator separately with the denominator to obtain the inverse Laplace transform.