Inverse Laplace Transform of an LTI with complex roots and s + real term in the numerator
\$x(t) = 2 cos( 2 \pi 30 t + 0.7) u( t )\$

\$x(t) = 2 cos( 0.7 )cos( 2 \pi 30 t + 0.7) u( t ) – 2 sin( 0.7 )sin( 2 \pi 30 t) u( t )\$

\$A=2cos(0.7)\$

\$B=-2sin(0.7)\$

\$a=0\$

\$X(s) = \frac{2 \cdot s \cdot cos(0.7) -2sin(0.7) \omega}{s^2+\omega^2} \cdot \frac{1}{s}\$

\$X(s) = 2 \frac{ cos(0.7)s -sin(0.7) \omega}{s^3+\omega^2 \cdot s}\$