Đáp án:

 \(x = 36\cos \left( {\dfrac{{5\pi }}{6}t - \dfrac{\pi }{6}} \right)\)

Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
\dfrac{T}{2} = 1,2s \Rightarrow T = 2,4s\\
 \Rightarrow \omega  = \dfrac{{2\pi }}{T} = \dfrac{{2\pi }}{{2,4}} = \dfrac{{5\pi }}{6}\left( {rad} \right)\\
{a_{\max }} = 25{\pi ^2}\left( {cm/{s^2}} \right)\\
A = \dfrac{{{a_{\max }}}}{{{\omega ^2}}} = \dfrac{{25{\pi ^2}}}{{\dfrac{{25}}{{36}}{\pi ^2}}} = 36\left( {cm} \right)\\
\Delta t = \dfrac{{1,2}}{3}.2 = 0,8s = \dfrac{T}{3}\\
 \Rightarrow \alpha  = \omega \Delta t = \dfrac{{5\pi }}{6}.0,8 = \dfrac{{2\pi }}{3}\\
 \Rightarrow {\varphi _{0a}} = \dfrac{{3\pi }}{2} - \dfrac{{2\pi }}{3} = \dfrac{{5\pi }}{6}\left( {rad} \right)\\
 \Rightarrow {\varphi _0} = {\varphi _{0a}} - \pi  = \dfrac{{5\pi }}{6} - \pi  =  - \dfrac{\pi }{6}\left( {rad} \right)\\
 \Rightarrow x = 36\cos \left( {\dfrac{{5\pi }}{6}t - \dfrac{\pi }{6}} \right)
\end{array}\)