11 A particle is suspended in a resistive medium from one end of a light spring. The other end of the spring is attached to a point which is made to oscillate in a vertical line. The displacement of the particle may be modelled by the differential equation \(\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 2 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 5 x = 10 \sin t\)
where \(x\) is the displacement of the particle below the equilibrium position at time \(t\).
When \(t = 0\) the particle is stationary and its displacement is 2 .

1. Find the particular solution of the differential equation.
2. Write down an approximate equation for the displacement when \(t\) is large.