Generating...                               quiz06_n27

  1. Find the Laplace transform for $\displaystyle f\left(t\right)=e^ {- t }\,\sin \left(3\,t\right)$

    $\displaystyle {{s+1}\over{s^2+2\,s+2}}$ $\displaystyle {{3}\over{s^2+2\,s+10}}$ $\displaystyle {{1}\over{s^2+2\,s+2}}$ $\displaystyle {{s+1}\over{s^2+2\,s+10}}$

  2. Find the inverse transform for $\displaystyle F\left(s\right)={{1}\over{2\,\left(s^2+9\right)}}-{{s^2}\over{ \left(s^2+9\right)^2}}$

    $\displaystyle {{\cos \left(3\,t\right)}\over{2}}$ $\displaystyle {{\sin \left(3\,t\right)}\over{6}}$ $\displaystyle -{{t\,\cos \left(3\,t\right)}\over{2}}$ $\displaystyle -{{t\,\sin \left(3\,t\right)}\over{6}}$

  3. Find the inverse transform for $\displaystyle F\left(s\right)={{s}\over{s^2-4\,s+13}}$

    $\displaystyle e^{2\,t}\,\left({{2\,\sin \left(3\,t\right)}\over{3}}+\cos \left(3 \,t\right)\right)$ $\displaystyle {{e^{2\,t}\,\sin \left(3\,t\right)}\over{3}}$ $\displaystyle {{5\,e^{5\,t}}\over{6}}+{{e^ {- t }}\over{6}}$ $\displaystyle {{e^{5\,t}}\over{6}}-{{e^ {- t }}\over{6}}$

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

    $\displaystyle \sin t$ $\displaystyle \cos t$ $\displaystyle {{\sin t}\over{2}}-{{t\,\cos t}\over{2}}$ $\displaystyle {{t\,\sin t}\over{2}}$

  5. Find the Laplace transform for $\displaystyle f\left(t\right)=\int_{0}^{t}{u\,\sin u\;du}$

    $\displaystyle {{1}\over{s^3-2\,s^2+2\,s}}$ $\displaystyle {{2}\over{s^4-2\,s^2+1}}$ $\displaystyle {{2}\over{s^4+2\,s^2+1}}$ $\displaystyle {{1}\over{s^3-2\,s^2}}$


Department of Mathematics
Last modified: 2026-09-10