Type 2 First Shifting Property Problem 6 - Laplace Transform - Engineering Mathematics 3

TL;DR

Expanding and applying Laplace transform using the first shifting property to solve problem number 6.

Transcript

welcome back friends in this video we'll be discussing laplace transform first shifting property problem number six welcome back friends let's discuss problem number six of first shifting property so let us move on see here the problem is one plus t e raised to minus t the whole cube so what needs to be done here first of all you need to expand thi... Read More

Key Insights

• 😑 The problem involves expanding a cube of a binomial expression.
• 🔨 Laplace transform provides a useful tool in solving problems involving differential equations.
• 🆘 The first shifting property helps in simplifying the calculations by shifting the 's' variable.
• ❓ Understanding the formulas for Laplace transform, such as for t^n, is crucial in solving such problems.
• 🏑 The Laplace transform is a powerful mathematical tool used in various fields, including control systems and signal processing.
• 🎮 The video emphasizes the importance of focusing and being careful while applying the Laplace transform and the first shifting property.
• 👻 Simplifying the Laplace transform results allows for easier analysis and further calculations.

Questions & Answers

Q: What is the initial problem being discussed in the video?

The initial problem is to expand (1 + te^-t)^3 using the cube formula.

Q: How is the Laplace transform applied to each term?

The Laplace transform is applied separately to each term by using the first shifting property. The exponential part of each term is ignored, and the remaining part is transformed based on the Laplace transform formula.

Q: What is the formula for Laplace transform of t^n?

The formula for Laplace transform of t^n is n factorial divided by s^(n+1).

Q: How is the Laplace transform result simplified?

After applying the Laplace transform to each term and shifting the 's' variable accordingly, the resulting terms are combined and written in their simplified form.

Summary & Key Takeaways

• The problem is to expand (1 + te^-t)^3 using the cube formula.

• The Laplace transform is applied to each term separately with the help of the first shifting property.

• The final result of the Laplace transform is obtained by simplifying the terms.