Problem 4 Based on Multiplication By 't' Property - Laplace Transform - Engineering Mathematics 3 | Summary and Q&A

TL;DR

Learn how to apply the multiplication by t property and the first shifting theorem to find the Laplace transform of complex functions.

Key Insights

• ✖️ The Laplace transform of a function can be calculated by utilizing the multiplication by t property and the first shifting theorem.
• 🛩️ The multiplication by t property simplifies the function by finding the derivative of the Laplace transform of a smaller function.
• 🆘 The first shifting theorem helps separate the function into exponential and trigonometric components.

Transcript

hi student so after completing the three problems on multiplication by t property let's move to the next problem on multiplication by t property and here we are gonna take the difficult problem and let's see how to apply the property to get the answer so let's start so here we have we have to find out the laplace transform of t into e to the power ... Read More

Questions & Answers

Q: What is the purpose of using the multiplication by t property in Laplace transform calculations?

The multiplication by t property simplifies the function by finding the derivative of the Laplace transform of a smaller function, reducing the number of steps and time required for calculations.

Q: Why is the first shifting theorem used in this problem?

The first shifting theorem helps separate the function into e^(3t) and t*sin(2t) components, allowing for a more straightforward application of the multiplication by t property.

Q: Can the Laplace transform be obtained by considering the function t as f(t) and applying the first shifting theorem first?

Yes, it is possible, but it may lead to a more complex expression for the Laplace transform, making calculations more time-consuming.

Q: What should be the preferred order of applying the multiplication by t property and the first shifting theorem?

It is recommended to apply the multiplication by t property first to simplify the function and then apply the first shifting theorem to find the Laplace transform in a more efficient manner.

Summary & Key Takeaways

• This video tutorial focuses on finding the Laplace transform of the function t*e^(3t)*sin(2t) using the multiplication by t property and the first shifting theorem.

• The first shifting theorem is used to simplify the function by considering e^(3t)tsin(2t) as e^(3t)(tsin(2t)).

• The multiplication by t property is then applied to calculate the Laplace transform using the derivative of the function.

• By following these steps, the final Laplace transform of the given function is obtained.