Generating...                               quiz06_n7

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

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

  2. Find the Laplace transform for $\displaystyle f\left(t\right)=t\,\cos t$

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

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

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

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

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

  5. Find the Laplace transform for $\displaystyle f\left(t\right)=t^4\,e^ {- 2\,t }$

    $\displaystyle {{2}\over{\left(s+2\right)^3}}$ $\displaystyle {{1}\over{s+2}}$ $\displaystyle {{2}\over{\left(s-2\right)^3}}$ $\displaystyle {{24}\over{\left(s+2\right)^5}}$ $\displaystyle {{24}\over{\left(s-2\right)^5}}$


Department of Mathematics
Last modified: 2025-06-19