Laplace Transforms

The Correct answer is option (B) : In Z/T

Step 1: Understanding the Concept:
We cannot directly compute the Laplace transform of using standard table entries. The best approach is to use the Taylor series expansion of the cosine function and then apply the Laplace transform term by term.
Step 2: Key Formula or Approach:
1. The Taylor series for is . 2. The Laplace transform of is for integer k.
Step 3: Detailed Explanation:
1. Expand using its Taylor series:
Substitute into the series for : 2. Apply the Laplace transform term by term:
Assuming we can interchange the sum and the integral: Now, use the transform for : . Step 4: Final Answer:
The Laplace transform is the series , which matches option (B).