Type 11 Second Shifting Problem 2,3 - Laplace Transform - Engineering Mathematics 3

TL;DR

This video discusses the application of the second shifting property to solve two problems, with step-by-step explanations and a clarification on the use of Laplace transform in interval problems.

Transcript

hello friends in this video we'll be discussing type number 11 second shifting property problem number two and three welcome back friends let's move on and let's discuss problem number two and three so without wasting time let's solve problem number two first of all let us check whether it is in the definition of second shifting property or not yes... Read More

Key Insights

• 🎮 The video demonstrates the step-by-step application of the second shifting property to solve problems involving Laplace transforms.
• 🅰️ It clarifies the different types of interval problems and explains the specific limit ranges associated with each type.
• 🎮 The video highlights the importance of being careful when solving interval problems and choosing the appropriate method, such as the second shifting property, rather than relying on the Laplace transform definition.
• 👻 The second shifting property allows for simplification and calculation of the Laplace transform by disregarding the shifting factor.

Questions & Answers

Q: How is problem number two solved using the second shifting property?

Problem number two is solved by applying the second shifting property and simplifying the equation by disregarding the shifting factor. The Laplace transform of e raised to t is then evaluated, resulting in the required solution.

Q: What is the approach to solving problem number three?

Problem number three is solved similarly to problem number two, but with the additional step of finding the Laplace transform of t cube. The Laplace transform of t raised to n is given by n factorial upon s raise to n+1, and applying this formula yields the solution for problem number three.

Q: Can the Laplace transform definition be used to solve interval problems?

No, the Laplace transform definition cannot be directly applied to interval problems. The video explains that interval problems fall into three types, with different limit ranges. Type number 9 has limits from 0 to infinity, type number 10 has limits from 0 to a, and type number 11 has limits from minus infinity to infinity.

Q: Why is the Laplace transform definition not applicable to type number 11 interval problems?

In type number 11 problems, the limits are from minus infinity to infinity. The Laplace transform definition, with the limits from 0 to infinity, cannot be used. Instead, the second shifting property must be employed due to the nature of the problem.

Summary & Key Takeaways

• The video focuses on solving problem number two by applying the second shifting property, simplifying the equation by forgetting the shifting factor, and obtaining the Laplace transform of e raised to t.

• Problem number three is solved similarly, but with the additional step of finding the Laplace transform of t cube.

• The video also addresses a common doubt about using the Laplace transform definition in interval type problems and explains the different types of interval problems.