7. $$\frac { \mathrm { d } ^ { 2 x } } { \mathrm {~d} t ^ { 2 } } + 3 \sin x = 0 . \quad \text { At } t = 0 , \quad x = 0 \quad \text { and } \quad \frac { \mathrm { d } x } { \mathrm {~d} t } = 0.4$$ (b) Find a series solution for \(x\), in ascending powers of \(t\), up to and including the term in \(t ^ { 3 }\).
(c) Use your answer to (b) to obtain an estimate of \(x\) at \(t = 0.3\).
(2)(Total 11 marks)