Quiz

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quiz05_n0

Find the inverse transform for $\displaystyle F\left(s\right)={{2}\over{\left(s-3\right)\,\left(s-2\right)\, \left(s+3\right)}}$
$\displaystyle {{e^{3\,t}}\over{3}}-{{2\,e^{2\,t}}\over{5}}+{{e^ {- 3\,t }}\over{ 15}}$ $\displaystyle {{e^{3\,t}}\over{2}}-{{2\,e^{2\,t}}\over{5}}-{{e^ {- 3\,t }}\over{ 10}}$ $\displaystyle {{5\,e^{3\,t}}\over{6}}-{{4\,e^{2\,t}}\over{5}}-{{e^ {- 3\,t } }\over{30}}$ $\displaystyle {{7\,e^{3\,t}}\over{6}}-e^{2\,t}-{{e^ {- 3\,t }}\over{6}}$ $\displaystyle {{e^{3\,t}}\over{6}}-{{e^{2\,t}}\over{5}}+{{e^ {- 3\,t }}\over{30}}$
Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{\left(s+2\right)\,\left(s^2+9\right)}}$
$\displaystyle {{2\,\sin \left(2\,t\right)}\over{13}}+{{3\,\cos \left(2\,t\right) }\over{13}}-{{3\,e^ {- 3\,t }}\over{13}}$ $\displaystyle {{2\,\sin \left(3\,t\right)}\over{39}}-{{\cos \left(3\,t\right) }\over{13}}+{{e^ {- 2\,t }}\over{13}}$ $\displaystyle {{3\,\sin \left(3\,t\right)}\over{13}}+{{2\,\cos \left(3\,t\right) }\over{13}}-{{2\,e^ {- 2\,t }}\over{13}}$ $\displaystyle {{3\,\sin \left(2\,t\right)}\over{26}}-{{\cos \left(2\,t\right) }\over{13}}+{{e^ {- 3\,t }}\over{13}}$
Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{4\,s^2+1}}$
$\displaystyle {{\cos \left({{t}\over{2}}\right)}\over{4}}$ $\displaystyle \cos \left(2\,t\right)$ $\displaystyle {{\sin \left(2\,t\right)}\over{2}}$ $\displaystyle {{\sin \left({{t}\over{2}}\right)}\over{2}}$
Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{s+4}}$
$\displaystyle {{e^ {- {{t}\over{4}} }}\over{4}}$ $\displaystyle e^ {- {{t}\over{4}} }$ $\displaystyle 4\,e^ {- 4\,t }$ $\displaystyle e^ {- 4\,t }$
Find the Laplace transform for f(t) = t(t + 3)
$\displaystyle -{{s-3}\over{s^2-3\,s+2}}$ $\displaystyle {{3\,s+2}\over{s^3}}$ $\displaystyle -{{s-2}\over{s^3}}$ $\displaystyle {{4\,s-7}\over{s^2-3\,s+2}}$ $\displaystyle -{{2\,s-2}\over{s^3}}$

Department of Mathematics
Last modified: 2026-07-16