Question

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

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

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 , $$\displaystyle{L}^{ -{{1}}}{\left\lbrace{Q}{\left({s}\right)}\right\rbrace}={L}^{ -{{1}}}{\left\lbrace\frac{s}{{{s}^{2}+{8}^{2}}}\right\rbrace}= \cos{{8}}{x}$$