Đáp án:

a) \( \pm \dfrac{{\sqrt 3 }}{2}\omega A\) ; \( \mp \dfrac{{{\omega ^2}A}}{2}\)

b) \( \pm \dfrac{{\sqrt 2 }}{2}\omega A\) ; \( \mp \dfrac{{{\omega ^2}A\sqrt 2 }}{2}\)

c) \( \pm \dfrac{{\omega A}}{2}\) ; \( \mp \dfrac{{{\omega ^2}A\sqrt 3 }}{2}\)

Giải thích các bước giải:

a) Ta có:

\(\begin{array}{l}
{x^2} + \dfrac{{{v^2}}}{{{\omega ^2}}} = {A^2} \Rightarrow \dfrac{{{A^2}}}{4} + \dfrac{{{v^2}}}{{{\omega ^2}}} = {A^2}\\
 \Rightarrow \dfrac{{{v^2}}}{{{\omega ^2}}} = \dfrac{3}{4}{A^2} \Rightarrow v =  \pm \dfrac{{\sqrt 3 }}{2}\omega A
\end{array}\)

Gia tốc là:

\(a =  - {\omega ^2}x =  \mp \dfrac{{{\omega ^2}A}}{2}\)

b) Ta có:

\(\begin{array}{l}
{x^2} + \dfrac{{{v^2}}}{{{\omega ^2}}} = {A^2} \Rightarrow \dfrac{{{A^2}}}{2} + \dfrac{{{v^2}}}{{{\omega ^2}}} = {A^2}\\
 \Rightarrow \dfrac{{{v^2}}}{{{\omega ^2}}} = \dfrac{1}{2}{A^2} \Rightarrow v =  \pm \dfrac{{\sqrt 2 }}{2}\omega A
\end{array}\)

Gia tốc là:

\(a =  - {\omega ^2}x =  \mp \dfrac{{{\omega ^2}A\sqrt 2 }}{2}\)

c) Ta có:

\(\begin{array}{l}
{x^2} + \dfrac{{{v^2}}}{{{\omega ^2}}} = {A^2} \Rightarrow \dfrac{{3{A^2}}}{4} + \dfrac{{{v^2}}}{{{\omega ^2}}} = {A^2}\\
 \Rightarrow \dfrac{{{v^2}}}{{{\omega ^2}}} = \dfrac{1}{4}{A^2} \Rightarrow v =  \pm \dfrac{{\omega A}}{2}
\end{array}\)

Gia tốc là:

\(a =  - {\omega ^2}x =  \mp \dfrac{{{\omega ^2}A\sqrt 3 }}{2}\)