Решение.\[ \begin{align}
& {{x}_{1}}=A\cdot \sin \omega \cdot {{t}_{1}}\ \ \ (1),\ {{x}_{2}}=A\cdot \sin \omega \cdot {{t}_{2}}\ \ \ (2), \\
& {{\varphi }_{2}}=2\cdot {{\varphi }_{1}},\ \omega \cdot {{t}_{2}}=2\cdot \omega \cdot {{t}_{1}}\ \ \ (3), \\
& \frac{{{x}_{1}}}{{{x}_{2}}}=\frac{A\cdot \sin \omega \cdot {{t}_{1}}}{A\cdot \sin \omega \cdot {{t}_{2}}}=\frac{\sin \omega \cdot {{t}_{1}}}{\sin 2\cdot \omega \cdot {{t}_{1}}}=\frac{\sin \omega \cdot {{t}_{1}}}{2\cdot \sin \omega \cdot {{t}_{1}}\cdot \cos \omega \cdot {{t}_{1}}}=\frac{1}{2\cdot \cos \omega \cdot {{t}_{1}}}\ \ \ (4), \\
& \cos \omega \cdot {{t}_{1}}=\frac{{{x}_{2}}}{2\cdot {{x}_{1}}},\ \sin \omega \cdot {{t}_{1}}=\sqrt{1-{{(\frac{{{x}_{2}}}{2\cdot {{x}_{1}}})}^{2}}}\ \ \ \ (5). \\
\end{align} \]
\[ A=\frac{{{x}_{1}}}{\sqrt{1-{{(\frac{{{x}_{2}}}{2\cdot {{x}_{1}}})}^{2}}}}\ \ \ \ (6). \]
А = 8,333 см.