Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{s^2+16}}$
$\displaystyle {{\sin \left({{t}\over{4}}\right)}\over{4}}$ $\displaystyle {{\cos \left({{t}\over{4}}\right)}\over{16}}$ $\displaystyle \cos \left(4\,t\right)$ $\displaystyle {{\sin \left(4\,t\right)}\over{4}}$
Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{4\,s+1}}$
$\displaystyle e^ {- 4\,t }$ $\displaystyle e^ {- {{t}\over{4}} }$ $\displaystyle {{e^ {- {{t}\over{4}} }}\over{4}}$ $\displaystyle 4\,e^ {- 4\,t }$
Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{\left(s-1\right)\,\left(s+1\right)\, \left(s+3\right)}}$
$\displaystyle {{e^{t}}\over{8}}+{{e^ {- t }}\over{4}}-{{3\,e^ {- 3\,t }}\over{8}}$ $\displaystyle {{e^{t}}\over{4}}+{{e^ {- t }}\over{2}}-{{3\,e^ {- 3\,t }}\over{4}}$ $\displaystyle {{3\,e^{t}}\over{8}}-{{e^ {- t }}\over{4}}-{{e^ {- 3\,t }}\over{8}}$ $\displaystyle {{3\,e^{t}}\over{8}}+{{e^ {- t }}\over{4}}-{{5\,e^ {- 3\,t }}\over{ 8}}$ $\displaystyle {{e^{t}}\over{4}}-{{e^ {- t }}\over{2}}+{{e^ {- 3\,t }}\over{4}}$
Find the Laplace transform for $\displaystyle f\left(t\right)=\cos \left(3\,t\right)+\sin t$
$\displaystyle {{3}\over{s^2+9}}+{{s}\over{s^2+1}}$ $\displaystyle {{s}\over{s^2-1}}+{{3}\over{s^2-9}}$ $\displaystyle {{s}\over{s^2+9}}+{{1}\over{s^2+1}}$ $\displaystyle {{1}\over{s^2-1}}+{{s}\over{s^2-9}}$
Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{s^2\,\left(s+1\right)}}$
$\displaystyle e^ {- t }+t-1$ $\displaystyle 1-e^ {- t }$ $\displaystyle \sin t$ $\displaystyle 1-\cos t$

Department of Mathematics
Last modified: 2023-10-13