Question

Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.)

L⁻¹ {1/s² - 2160/s⁷}

Answer 1

The inverse Laplace transform of the given function is calculated using the theorem for the Laplace transform of a power of t..The inverse Laplace transform of 1/s² - 2160/s⁷ is t.

Step-by-step explanation:

To find the inverse Laplace transform of 1/s² - 2160/s⁷, we can use Theorem 7.2.1. This theorem states that

L⁻¹{F(s-a)} = e^at L⁻¹{F(s)}, where a is a constant and F(s) is the Laplace transform of a function f(t).

Applying this theorem to our problem, we have L⁻¹{1/s² - 2160/s⁷} = e^at L⁻¹{1/s²}, where a = 0 and L⁻¹{1/s²} is the inverse Laplace transform of 1/s².

The inverse Laplace transform of 1/s² is t, so the solution to our problem is t * e^0t = t.