Đáp án:

 \(A = \dfrac{{2\pi \sqrt 3 }}{3}\left( {cm} \right)\)

Giải thích các bước giải:

Ta có: 

\(\begin{array}{l}
T = \dfrac{1}{f} = \dfrac{1}{2} = 0,5s\\
 \Rightarrow \omega  = \dfrac{{2\pi }}{T} = \dfrac{{2\pi }}{{0,5}} = 4\pi \left( {rad/s} \right)\\
t = \dfrac{1}{6}s = \dfrac{T}{3}\\
 \Rightarrow \alpha  = \omega t = \dfrac{{2\pi }}{T}.\dfrac{T}{3} = \dfrac{{2\pi }}{3}\left( {rad} \right)\\
\beta  = \dfrac{\alpha }{4} = \dfrac{{2\pi }}{{3.4}} = \dfrac{\pi }{6}\left( {rad} \right)\\
\cos \beta  = \dfrac{v}{{{v_{\max }}}} \Rightarrow \cos \dfrac{\pi }{6} = \dfrac{4}{{\omega A}}\\
 \Rightarrow \dfrac{{\sqrt 3 }}{2} = \dfrac{4}{{4\pi .A}} \Rightarrow A = \dfrac{{2\pi \sqrt 3 }}{3}\left( {cm} \right)
\end{array}\)