inverse laplace 1/s^2 — step-by-step solution

Find the causal inverse transform, for t ≥ 0. By linearity, invert each partial fraction

The inverse Laplace formula for

\frac{1}{{(s - a)}^{n}}

t^{n - 1} \cdot \frac{\exp (a t)}{(n - 1)!}

; it gives for

\frac{1}{s^{2}}

\frac{t \exp (0 \cdot t)}{1!}

⇥ⓘ A product with a zero factor is zero:

0 \cdot t

0

■Any nonzero number raised to the power 0 is 1:

\exp (0)

1

■The factorial of a number is the product of all the integers from 1 to that number:

1!

1

⇥

\frac{t}{1}

▶Inverse Laplace transform:

t