The differential equation $$\[ \frac{\mathrm{d}^{2} x}{\mathrm{~d} t^{2}}+6 \frac{\mathrm{d} x}{\mathrm{~d} t}+13 x=8 \mathrm{e}^{-3 t} \quad t \geqslant 0 \]$$ describes the motion of a particle along the $$\(x\)$$-axis. On the graph of the particular solution found in part (b), the first turning point for $$\(t> 0\)$$ occurs at $$\(x=a\)$$. (c) Determine, to 3 significant figures, the value of $$\(a\)$$. [Solutions relying entirely on calculator technology are not acceptable.] (4)

Answer:

Knowledge points:

Solution: