Find the general solution of the differential equation
\(\frac{\mathrm{d}^{2} x}{\mathrm{~d} t^{2}}+4 \frac{\mathrm{~d} x}{\mathrm{~d} t}+4 x=\sin 2 t\)

Describe the behaviour of \(x\) as \(t \rightarrow \infty\), justifying your answer.