Type 4 Effect of Division By t Problem 3 - Laplace Transform - Engineering Mathematics 3

TL;DR

This video discusses the effect of division by t in Laplace transform problems, providing step-by-step explanations and examples.

Transcript

hello friends in this video we'll be discussing effect of division by t problem number three welcome back friends now we are discussing the third problem cos h 2 t sine square 2 t upon t so this is our third problem do you remember the note whenever you get a question from laplace transform the first thing that should come in your mind is note and ... Read More

Key Insights

• ❓ Hyperbolic functions in Laplace transform problems should be converted into exponential functions.
• 🍉 Dividing by t simplifies the problem by isolating specific terms.
• 👨‍💼 Solving for the Laplace transform of sine functions requires converting them into linear terms.

Questions & Answers

Q: What is the first step to take when solving a Laplace transform problem?

The first step is to convert hyperbolic functions into exponential functions. This is done by replacing cosh(2t) with (e^(2t) + e^(-2t))/2.

Q: How can the problem cosh(2t)sin^2(2t)/t be simplified further?

By applying the effect of division by t and focusing on each term individually. In this case, only sin^2(2t) remains, which can be simplified as 1 - cos^2(2t).

Q: How do you find the Laplace transform of sin^2(2t)?

By converting sin^2(2t) into a linear term, it becomes 1 - cos(4t)/2. The Laplace transform of sin^2(2t) is equivalent to the Laplace transform of sin^2(t), which is 1/4s - s/(s^2 + 16).

Q: What is the final solution for the given problem?

The final solution is 1/8 * log[(s-2)^2 + 16]/[(s-2)^2] + log[(s+2)^2 + 16]/[(s+2)^2].

Summary & Key Takeaways

• The video discusses problem number three, which involves cosh(2t)sin^2(2t)/t.

• It emphasizes the importance of converting hyperbolic functions into exponential functions when dealing with Laplace transforms.

• The problem is simplified by converting cosh(2t) into (e^(2t) + e^(-2t))/2 and solving for sin^2(2t).