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

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

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

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

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

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

  4. Find the Laplace transform for f(t) = (t − 2)t

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

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

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


Department of Mathematics
Last modified: 2025-08-10