Laplace transform $(10$ points$)$

Using the properties of Laplace transform in Table $12-1$ and the Laplace transform pairs in Table $12-2,$ determine the Laplace transform of the following waveforms.

$($a$)(1$ point$)f(t)=4t{e}^{-2t}u(t)$

$($b$)(1$ point$)f(t)=10cos(12t+60)u(t)$

$($c$)(1$ point$)f(t)=16e^{-2t}cos(4t)u(t)$

$($d$)(1$ point$)f(t)=4e^{-2(t-3)}u(t-4)$

$($e$)(1$ point$)f(t)=27t^{2}sin(6t-60)u(t)$

$($f$)(1$ point$)f(t)=10\frac{sin(3t)}{t}u(t)$

$($g$)(1$ point$)f(t)=t^2[u(t)-u(t-4)]$

$($h$)(1$ point$)f(t)=\frac{d^2}{d{t}^2}[e^{-4t}u(t)]$

$($i$)(1$ point$)f(t)=25cos(4t+30)(t)$

$($j$)(1$ point$)f(t)=25cos(4t+30)(t-0\mathrm{.}2)$