Generating...                               quiz06_n22

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

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

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

    $\displaystyle {{t^3\,e^ {- t }}\over{6}}$ $\displaystyle {{t^2\,e^{t}}\over{2}}+t\,e^{t}$ $\displaystyle t\,e^ {- t }-{{t^2\,e^ {- t }}\over{2}}$ $\displaystyle {{t^3\,e^{t}}\over{6}}$

  3. Find the Laplace transform for $\displaystyle f\left(t\right)=\int_{0}^{t}{u\,\sinh \left(2\,u\right)\;du}$

    $\displaystyle {{4}\over{s^4-8\,s^2+16}}$ $\displaystyle {{2}\over{s^3-2\,s^2-3\,s}}$ $\displaystyle {{2\,s}\over{s^4+8\,s^2+16}}-{{1}\over{s^3+4\,s}}$ $\displaystyle {{s}\over{s^3-2\,s^2+5\,s}}-{{1}\over{s^3-2\,s^2+5\,s}}$

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

    $\displaystyle {{\sin \left(4\,t\right)}\over{8}}$ $\displaystyle -{{t\,\sin \left(4\,t\right)}\over{8}}$ $\displaystyle {{\cos \left(4\,t\right)}\over{2}}$ $\displaystyle -{{t\,\cos \left(4\,t\right)}\over{2}}$

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

    $\displaystyle {{2\,s^2}\over{s^4+8\,s^2+16}}-{{1}\over{s^2+4}}$ $\displaystyle {{s}\over{s^2-2\,s-3}}-{{1}\over{s^2-2\,s-3}}$ $\displaystyle {{s}\over{s^2-2\,s+5}}-{{1}\over{s^2-2\,s+5}}$ $\displaystyle {{2\,s^2}\over{s^4-8\,s^2+16}}-{{1}\over{s^2-4}}$


Department of Mathematics
Last modified: 2026-07-16