Problem 2 Based on Inverse Laplace Transform using Standard Results - Engineering Mathematics 3

TL;DR

Solving an infinite series using Inverse Laplace Transform with Maclaurin series for cos x.

Transcript

hello friends so after covering the numerical on the standard properties or i would say the standard formulae of inverse laplace transform let's do one more numerical on the formula of inverse laplace transform so here i've taken a different function of s and let's see how to get value of that so here we have to find out laplace inverse of 1 upon s... Read More

Key Insights

• ☺️ Maclaurin series for cos x is crucial in simplifying functions for Inverse Laplace Transform.
• 👻 Linearity property allows for separate analysis of terms in the Inverse Laplace Transform.
• 🥺 Understanding standard results of Inverse Laplace Transform leads to accurate solutions.

Questions & Answers

Q: What function is being evaluated using the Inverse Laplace Transform in the example?

The function 1/s * cos(1/s) is being evaluated in the example, requiring the use of Maclaurin series for cos x.

Q: How is the Maclaurin series for cos x utilized in the calculation?

The Maclaurin series for cos x, which involves even terms with alternating signs, is substituted with 1/s in place of x to simplify the function.

Q: How is the linearity property of Inverse Laplace Transform applied in the solution?

The linearity property allows for solving each term separately when applying Inverse Laplace Transform to an expression with terms separated by plus or minus signs.

Q: What is the final expression found for the Inverse Laplace Transform in the example?

The final expression results in an infinite series representation after simplifying the function using the Maclaurin series and applying the linearity property.

Summary & Key Takeaways

• In this tutorial, an example of finding the Inverse Laplace Transform of 1/s * cos(1/s) is demonstrated.

• The function is simplified using Maclaurin series for cos x, yielding an infinite series.

• Linearity property of Inverse Laplace Transform is applied to find the final expression for the inverse transform.