Question

For an input forcing function, \( X(t) = 2t^2 \), the Laplace transform of this function is

• A. \( \frac{2}{s^2} \)
• B. \( \frac{4}{s^3} \)
• C. \( \frac{2}{s^3} \)
• D. \( \frac{4}{s^2} \)

Hint:

Use standard Laplace transforms for polynomial time functions.

Answer 1

The Correct Option is B

Using Laplace transform formula: \( \mathcal{L}\{t^n\} = \frac{n!}{s^{n+1}} \).
For \( n=2 \), \( \mathcal{L}\{2t^2\} = 2 \times \frac{2!}{s^3} = \frac{4}{s^3} \).