Consider the function $$f(t) = \left\lbrace \begin{array}{ l l } 0 & \mbox{ if } 0\leq t < 4\pi \\ \sin(t - 4\pi) & \mbox{ if } 4\pi \leq t. \end{array} \right.$$

1. Use the graph of this function to write it in terms of the Heaviside function. Use $h(t-a)$ for the Heaviside function shifted $a$ units horizontally.
   
   $f(t) =$ help (formulas)
   
   
2. Find the Laplace transform $F(s) = {\mathcal L}\left\lbrace f(t) \right\rbrace$.
   
   $\displaystyle F(s) = {\mathcal L}\left\lbrace f(t) \right\rbrace =$ help (formulas)