Question

determine the inverse Laplace transform of the function. displaystyle{Q}{left({s}right)}=frac{s}{{{s}^{2}+{64}}}

Laplace transform
ANSWERED
asked 2020-11-09
determine the inverse Laplace transform of the function.
\(\displaystyle{Q}{\left({s}\right)}=\frac{s}{{{s}^{2}+{64}}}\)

Answers (1)

2020-11-10
Step 1
Given that
\(\displaystyle{Q}{\left({s}\right)}=\frac{s}{{{s}^{2}+{64}}}\)
\(\displaystyle=\frac{s}{{{s}^{2}+{8}^{2}}}\)
Step 2
Now, inverse Laplace transform of the function is,
Since , \(\displaystyle{L}^{ -{{1}}}{\left\lbrace\frac{s}{{{s}^{2}+{a}^{2}}}\right\rbrace}= \cos{{a}}{x}\)
Hence , \(\displaystyle{L}^{ -{{1}}}{\left\lbrace{Q}{\left({s}\right)}\right\rbrace}={L}^{ -{{1}}}{\left\lbrace\frac{s}{{{s}^{2}+{8}^{2}}}\right\rbrace}= \cos{{8}}{x}\)
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