Final answer:
To find the inverse Laplace transform of H(s) using partial fraction expansion, one must factor the quartic polynomial in the denominator, express H(s) into partial fractions, and then apply inverse Laplace transforms to each term individually.
Step-by-step explanation:
To find the inverse Laplace transform of the given function H(s), you would perform a partial fraction expansion of H(s) = (10^15 s) / (s^4 + 22000s^3 + 141 x 10^6 s^2 + 220 x 10^9s + 10^14). However, the process for this particular function can become quite complex, as it may involve finding the roots of a quartic polynomial, which in itself could require numerical methods if the roots cannot be factored easily or are not real numbers.
Once the roots are determined, you can proceed to express H(s) in terms of partial fractions, where each term is in the form of A/(s - s_0), B/(s - s_1), C/(s - s_2), ..., with s_0, s_1, s_2, ..., being the roots of the denominator. After separating H(s) into partial fractions, you can then apply the inverse Laplace transform to each fraction individually using standard Laplace transform tables or theorems. The result would be a sum of functions of time t, representing the original time-domain signal.