(Solved): (1 point) Consider the function \[ f(t)=\left\{\begin{array}{ll} 0 & \text { if } 0 \leq t ...

(1 point) Consider the function \[ f(t)=\left\{\begin{array}{ll} 0 & \text { if } 0 \leq t<4 \pi \\ \sin (t-4 \pi) & \text { if } 4 \pi \leq t \end{array}\right. \] a. 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. \( f(t) \) elp (formulas) b. Find the Laplace transform \( F(s)=\mathcal{L}\{f(t)\} \). \( F(s)=\mathcal{L}\{f(t)\}= \) help (formulas)