Question

Compute the inverse laplace transform of 7/(s-1)^3​

Answer 1

Step-by-step explanation:

Given:

$\frac{7}{ {(s- 1)}^{3} }$

To find: Compute inverse Laplace of given function.

Solution:

Formula used:

$\bold{\red{ {£}^{ - 1} \left( \frac{1}{(s - a)^{n} } \right) = \frac{ {e}^{at} {t}^{n - 1} }{(n - 1)!} }}$

Use the above formula

${£}^{ - 1} \left( \frac{7}{(s - 1)^{3} } \right) = \frac{ 7{e}^{t} {t}^{3 - 1} }{(3- 1)!} \\ \\ {£}^{ - 1} \left( \frac{7}{(s - 1)^{3} } \right) = \frac{ 7{e}^{t} {t}^{2} }{(2)!} \\ \\ {£}^{ - 1} \left( \frac{7}{(s - 1)^{3} } \right) = \frac{ 7{e}^{t} {t}^{2} }{2}$

Final answer:

$\bold{\green{{£}^{ - 1} \left( \frac{7}{(s - 1)^{3} } \right) = \frac{ 7{e}^{t} {t}^{2} }{2}}}$

Hope it helps you.

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