Dao động của một chất điểm là tổng hợp của hai dao động

* Hướng dẫn giải

Đáp án B

Phương trình dao động tổng hợp: $\text{x}={\text{x}}_{\text{1}}+{\text{x}}_{\text{2}}=6\cos \left(\frac{\text{2π}}{\text{3}}t-\frac{\text{π}}{\text{6}}\right)\text{cm}$

Tại thời điểm ${\text{x}}_{\text{1}}={\text{x}}_{\text{2}}\iff$$3\cos \left(\frac{\text{2π}}{\text{3}}\text{t}-\frac{\text{π}}{\text{2}}\right)-3\sqrt{3}\text{\hspace{0.17em}cos}\left(\frac{\text{2π}}{\text{3}}\text{t}\right)=0\iff 3\cos \left(\frac{\text{2π}}{\text{3}}\text{t}-\frac{\text{π}}{\text{2}}\right)+3$

$\sqrt{3}\sin \left(\frac{\text{2π}}{\text{3}}\text{t}-\frac{\text{π}}{\text{2}}\right)=0$

$$\begin{gathered} \iff 3.2\left[\frac{1}{2}c\text{os}\left(\frac{\text{2π}}{\text{3}}\text{t}-\frac{\text{π}}{\text{2}}\right)+\frac{\sqrt{3}}{2}\sin \left(\frac{\text{2π}}{\text{3}}\text{t}-\frac{\text{π}}{\text{2}}\right)\right]=0 \\ \iff 6\cos \left(\frac{\text{2π}}{\text{3}}\text{t}-\frac{\text{π}}{\text{2}}-\frac{\text{π}}{3}\right)=0 \\ \iff \left(\frac{\text{2π}}{\text{3}}\text{t}-\frac{\text{5π}}{\text{6}}\right)=\pm \frac{\text{π}}{\text{2}}+2\text{kπ} \\ \iff \left\{\begin{array}{l}\frac{\text{2π}}{\text{3}}\text{t}=\frac{\text{π}}{3}+\text{k}2\text{π}\\ \frac{\text{2π}}{\text{3}}\text{t}=\frac{\text{4π}}{3}+\text{k}2\text{π}\end{array}\right. \\ \Rightarrow \text{x}=\pm 3\sqrt{3}\approx \pm 5,19\text{cm} \end{gathered}$$