Câu 3: 

a) Ta có: 

\(\begin{array}{l}
v = 20\pi \cos \left( {2\pi t + \dfrac{\pi }{3}} \right) \Rightarrow \left\{ \begin{array}{l}
{v_{\max }} = 20\pi \left( {cm/s} \right)\\
\omega  = 2\pi \left( {rad/s} \right)
\end{array} \right.\\
T = \dfrac{{2\pi }}{\omega } = \dfrac{{2\pi }}{{2\pi }} = 1\left( s \right)\\
f = \dfrac{1}{T} = 1Hz\\
A = \dfrac{\omega }{\omega } = \dfrac{{20\pi }}{{2\pi }} = 10\left( {cm} \right)
\end{array}\)

b) Biểu thức li độ là:

\(x = 10\cos \left( {2\pi t - \dfrac{\pi }{6}} \right)\)

Bài 4: 

a) Ta có: 

\(\begin{array}{l}
A = \dfrac{{20}}{2} = 10\left( {cm} \right)\\
T = \dfrac{{25}}{{50}} = 0,5s\\
f = \dfrac{1}{T} = \dfrac{1}{{0,5}} = 2Hz
\end{array}\)

b) Ta có: 

\(\begin{array}{l}
a =  - {\omega ^2}x =  - {\left( {4\pi } \right)^2}.\left( { - 3} \right) = 64{\pi ^2}\left( {cm/{s^2}} \right)\\
{x^2} + {\left( {\dfrac{v}{\omega }} \right)^2} = {A^2}\\
 \Rightarrow 9 + {\left( {\dfrac{v}{{4\pi }}} \right)^2} = {10^2}\\
 \Rightarrow v = 4\pi \sqrt {91} \left( {m/s} \right)
\end{array}\)