inverse laplace transform, example 3  Summary and Q&A
TL;DR
This content explains how to calculate the Laas transform for expressions involving S  3 and S + 10.
Questions & Answers
Q: How can the Laas transform be calculated for expressions involving S  3?
To calculate the Laas transform for expressions with S  3, multiply the Laas transform of cosine BT by e^(3 t) and replace S with S  3. This will give us (S  3) / ((S  3)^2 + B S^2).
Q: What if the expression involves S + 10 instead of S  3?
If the expression involves S + 10, we can still use the same method by replacing S with S  a. In this case, add 3 to both sides of the expression to make it S  3. The resulting Laas transform will be (S  3) / ((S  3)^2 + B S^2).
Q: How can the Laas transform be calculated for expressions involving a constant on the top?
If there is a constant on the top of the expression, use the formula for the Laas transform of s BT, which is equal to B / (S^2 + B S). Multiply the top by the constant, and divide the equation by the constant to maintain the same values. This will give us the appropriate Laas transform.
Q: How do we handle the situation when the expressions involve a constant and S  3 or S + 10?
To handle the situation involving a constant on the top and S  3 or S + 10, use the formula for the Laas transform of s BT and multiply the top by the constant. Be sure to divide by the constant as well to cancel it out. This will give us the correct Laas transform.
Summary & Key Takeaways

The Laas transform of cosine BT is equal to S / (S^2 + B S), but if it involves S  3, it needs to be translated by multiplying with e^(a t) and replacing S with S  a.

The explanation shows how to calculate the Laas transform for expressions involving S  3 and S + 10 by using the appropriate formula and shifting the variables.

If the expression involves S + 10 instead of S  3, the same method can be applied by replacing S with S  a and shifting it accordingly.