Find the particular solution of the differential equation
\[\frac{\mathrm{d}^{2} x}{\mathrm{~d} t^{2}}+8 \frac{\mathrm{~d} x}{\mathrm{~d} t}+15 x=102 \cos 3 t\]
given that, when \(t=0, x=1\) and \(\frac{\mathrm{d} x}{\mathrm{~d} t}=0\).