Đáp án:

a) \(a =  - 80{\pi ^2}\cos \left( {2\pi t - \dfrac{\pi }{3}} \right)\)

b) 

\(\begin{array}{l}
{v_{\max }} = 40\pi \left( {cm/s} \right)\\
{a_{\max }} = 80{\pi ^2}\left( {c{m^2}/s} \right)
\end{array}\)

Giải thích các bước giải:

a) Ta có: 

\(\begin{array}{l}
A = \dfrac{l}{2} = \dfrac{{40}}{2} = 20cm\\
{x^2} + {\left( {\dfrac{v}{\omega }} \right)^2} = {A^2}\\
 \Rightarrow {10^2} + {\left( {\dfrac{{20\pi \sqrt 3 }}{\omega }} \right)^2} = {20^2}\\
 \Rightarrow \omega  = 2\pi \left( {rad/s} \right)\\
\cos \varphi  = \dfrac{x}{A} = \dfrac{{10}}{{20}} = \dfrac{1}{2} \Rightarrow \varphi  =  - \dfrac{\pi }{3}\left( {rad} \right)\\
 \Rightarrow x = 20\cos \left( {2\pi t - \dfrac{\pi }{3}} \right)\\
 \Rightarrow v =  - 40\pi \sin \left( {2\pi t - \dfrac{\pi }{3}} \right)\\
 \Rightarrow a =  - 80{\pi ^2}\cos \left( {2\pi t - \dfrac{\pi }{3}} \right)
\end{array}\)

b) Ta có: 

\(\begin{array}{l}
{v_{\max }} = 40\pi \left( {cm/s} \right)\\
{a_{\max }} = 80{\pi ^2}\left( {c{m^2}/s} \right)
\end{array}\)