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Câu hỏi: Hai dao động điều hòa thành phần cùng phương cùng tần số có phương trình $\mathrm{x}_{1}=\mathrm{A}_{1} \cos \left(\omega \mathrm{t}+\dfrac{\pi}{2}\right)(\mathrm{cm})$ và $\mathrm{x}_{2}=\mathrm{A}_{2} \cos \left(\omega \mathrm{t}-\dfrac{\pi}{4}\right)(\mathrm{cm})$. Biết phương trình dao động tổng họp là $\mathrm{x}=5 \cos (\omega \mathrm{t}+\varphi)(\mathrm{cm})$. Để $\left(\mathrm{A}_{1}+\mathrm{A}_{2}\right)$ có giá trị cực đại thì $\varphi$ có giá trị là:
A. $\dfrac{\pi}{6}$
B. $\dfrac{\pi}{24}$
C. $\dfrac{\pi }{8}$
D. $\dfrac{\pi}{12}$
$\Rightarrow \dfrac{5}{\sin \left( \dfrac{\pi }{2}+\dfrac{\pi }{4} \right)}=\dfrac{{{A}_{1}}}{\sin \left( \varphi +\dfrac{\pi }{4} \right)}=\dfrac{{{A}_{2}}}{\sin \left( \dfrac{\pi }{2}-\varphi \right)}=\dfrac{{{A}_{1}}+{{A}_{2}}}{\sin \left( \varphi +\dfrac{\pi }{4} \right)-\sin \left( \varphi -\dfrac{\pi }{2} \right)}\underset{1\angle \dfrac{\pi }{4}-1\angle -\dfrac{\pi }{2}}{\mathop{=}} \dfrac{{{A}_{1}}+{{A}_{2}}}{1,848\sin \left( \varphi +\dfrac{3\pi }{8} \right)}$
$\Rightarrow {{\left( {{A}_{1}}+{{A}_{2}} \right)}_{\max }}$ khi $\sin \left( \varphi +\dfrac{3\pi }{8} \right)=1\Rightarrow \varphi =\dfrac{\pi }{8}$.
A. $\dfrac{\pi}{6}$
B. $\dfrac{\pi}{24}$
C. $\dfrac{\pi }{8}$
D. $\dfrac{\pi}{12}$
$\dfrac{A}{\sin \left( {{\varphi }_{1}}-{{\varphi }_{2}} \right)}=\dfrac{{{A}_{1}}}{\sin \left( \varphi -{{\varphi }_{2}} \right)}=\dfrac{{{A}_{2}}}{\sin \left( {{\varphi }_{1}}-\varphi \right)}$ $\Rightarrow \dfrac{5}{\sin \left( \dfrac{\pi }{2}+\dfrac{\pi }{4} \right)}=\dfrac{{{A}_{1}}}{\sin \left( \varphi +\dfrac{\pi }{4} \right)}=\dfrac{{{A}_{2}}}{\sin \left( \dfrac{\pi }{2}-\varphi \right)}=\dfrac{{{A}_{1}}+{{A}_{2}}}{\sin \left( \varphi +\dfrac{\pi }{4} \right)-\sin \left( \varphi -\dfrac{\pi }{2} \right)}\underset{1\angle \dfrac{\pi }{4}-1\angle -\dfrac{\pi }{2}}{\mathop{=}} \dfrac{{{A}_{1}}+{{A}_{2}}}{1,848\sin \left( \varphi +\dfrac{3\pi }{8} \right)}$
$\Rightarrow {{\left( {{A}_{1}}+{{A}_{2}} \right)}_{\max }}$ khi $\sin \left( \varphi +\dfrac{3\pi }{8} \right)=1\Rightarrow \varphi =\dfrac{\pi }{8}$.
Đáp án C.