Sketch or describe solution behavior

6 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.

4 The solution of a second order differential equation is \(\mathrm { f } ( t )\) The differential equation models heavy damping.
Which one of the statements below could be true?
Tick ( \(\checkmark\) ) one box. $$\begin{aligned} & \mathrm { f } ( t ) = 2 \mathrm { e } ^ { - t } \cos ( 3 t ) + 5 \mathrm { e } ^ { - t } \sin ( 3 t ) \\ & \mathrm { f } ( t ) = 3 \mathrm { e } ^ { - t } + 4 t \mathrm { e } ^ { - t } \\ & \mathrm { f } ( t ) = 7 \mathrm { e } ^ { - t } + 2 \mathrm { e } ^ { - 2 t } \\ & \mathrm { f } ( t ) = 8 \mathrm { e } ^ { - t } \cos ( 3 t - 0.1 ) \end{aligned}$$ □
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