Generating...                               quiz05_n17

  1. Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{s^2\,\left(s+1\right)}}$

    $\displaystyle 1-\cos t$ $\displaystyle e^ {- t }+t-1$ $\displaystyle \sin t$ $\displaystyle 1-e^ {- t }$

  2. Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{16\,s^2+1}}$

    $\displaystyle {{\sin \left(4\,t\right)}\over{4}}$ $\displaystyle \cos \left(4\,t\right)$ $\displaystyle {{\sin \left({{t}\over{4}}\right)}\over{4}}$ $\displaystyle {{\cos \left({{t}\over{4}}\right)}\over{16}}$

  3. Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{\left(s-1\right)\,\left(s+1\right)\, \left(s+3\right)}}$

    $\displaystyle {{e^{t}}\over{8}}+{{e^ {- t }}\over{4}}-{{3\,e^ {- 3\,t }}\over{8}}$ $\displaystyle {{3\,e^{t}}\over{8}}+{{e^ {- t }}\over{4}}-{{5\,e^ {- 3\,t }}\over{ 8}}$ $\displaystyle {{3\,e^{t}}\over{8}}-{{e^ {- t }}\over{4}}-{{e^ {- 3\,t }}\over{8}}$ $\displaystyle {{e^{t}}\over{4}}+{{e^ {- t }}\over{2}}-{{3\,e^ {- 3\,t }}\over{4}}$ $\displaystyle {{e^{t}}\over{4}}-{{e^ {- t }}\over{2}}+{{e^ {- 3\,t }}\over{4}}$

  4. Find the Laplace transform for $\displaystyle f\left(t\right)=\cos \left(3\,t\right)+\sin t$

    $\displaystyle {{s}\over{s^2-1}}+{{3}\over{s^2-9}}$ $\displaystyle {{s}\over{s^2+9}}+{{1}\over{s^2+1}}$ $\displaystyle {{1}\over{s^2-1}}+{{s}\over{s^2-9}}$ $\displaystyle {{3}\over{s^2+9}}+{{s}\over{s^2+1}}$

  5. Find the Laplace transform for $\displaystyle f\left(t\right)=\left(e^{t}-2\right)\,e^{t}$

    $\displaystyle -{{s-6}\over{s^2-6\,s+8}}$ $\displaystyle -{{s-3}\over{s^2-3\,s+2}}$ $\displaystyle {{4\,s-7}\over{s^2-3\,s+2}}$ $\displaystyle {{1}\over{s^2-3\,s+2}}$ $\displaystyle {{4\,s-14}\over{s^2-6\,s+8}}$


Department of Mathematics
Last modified: 2026-03-24