Find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 10 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 25 x = 338 \sin t$$
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Show that, for large positive values of \(t\) and for any initial conditions,
$$x \approx R \sin ( t - \phi ) ,$$
where the constants \(R\) and \(\phi\) are to be determined.