The inverse Laplace transform of $F ( s ) = ( 5 s + 2 ) / \left( s ^ { 2 } \cdot \left( s ^ { 2 } - 1 \right) \right)$ is
A) $- 5 - 2 t + 7 e ^ { t } / 2 + 3 e ^ { - t } / 2$
B) $5 - 2 t - 7 e ^ { t } / 2 + 3 e ^ { - t } / 2$
C) $5 - 2 t + 7 e ^ { t } / 2 + 3 e ^ { - t } / 2$
D) $- 5 + 2 t - 7 e ^ { t } / 2 + 3 e ^ { - t } / 2$
E) $- 5 + 2 t + 7 e ^ { t } / 2 + 3 e ^ { - t } / 2$

Question

Quizplus · Accepted Answer

The inverse Laplace transform of $F(s) = \frac{5s + 2}{s^2(s^2 - 1)}$ can be found by partial fraction decomposition and using standard Laplace transform pairs. The correct inverse transform, considering the structure of the given options, matches option A, which includes terms corresponding to a constant, a linear term in $t$, and exponential terms for $e^t$ and $e^{-t}$, correctly accounting for the poles of $F(s)$ at $s = 0$ and $s = \pm 1$.

The Inverse Laplace Transform Of F(s)=(5s+2)/(s2⋅(s2−1))F ( s ) = ( 5 s + 2 ) / \left( s ^ { 2 } \cdot \left( s ^ { 2 } - 1 \right) \right)F(s)=(5s+2)/(s2⋅(s2−1))

The Inverse Laplace Transform Of $F ( s ) = ( 5 s + 2 ) / \left( s ^ { 2 } \cdot \left( s ^ { 2 } - 1 \right) \right)$