Question
Determine a function $f(t)$ that has the given Laplace transform $F(s)$.$$F(s)=\frac{2}{s\left(s^{2}+16\right)}$$
Step 1
We write $$\frac{2}{s(s^{2}+16)} = \frac{A}{s} + \frac{Bs+C}{s^{2}+16}.$$ Multiplying through by the denominator, we get $$2 = A(s^{2}+16) + s(Bs+C).$$ Expanding and collecting terms, we get $$2 = (A+B)s^{2} + Cs + 16A.$$ Show more…
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