\(t=\dfrac{\dfrac{\pi}{6}}{\dfrac{2\pi}{T}}=\dfrac{1}{4}\left(s\right)\)

\(W=0,04=mgl\left(1-\cos\alpha_0\right)\)

\(\Leftrightarrow\cos\alpha_0=\dfrac{239}{240}\Rightarrow\alpha_0=....\)

\(T=mg\left(3\cos\alpha-2\cos\alpha_0\right)\)

Lực căng dây cực tiểu khi nó ở biên, nghĩa là \(\alpha=\alpha_0\)

\(\Rightarrow T_{min}=mg\cos\alpha_0\)

\(T=2T_{min}\Leftrightarrow mg\left(3\cos\alpha-2\cos\alpha_0\right)=2mg\cos\alpha_0\)\(\Leftrightarrow\cos\alpha=\dfrac{4}{3}\cos\alpha_0\)

\(W_t=mgl\left(1-\cos\alpha\right)=mgl\left(1-\dfrac{4}{3}\cos\alpha_0\right)\)

\(T=2\pi\sqrt{\dfrac{m}{k}};T'=2\pi\sqrt{\dfrac{m}{k'}};k.l=k'.l'\Leftrightarrow\dfrac{k}{k'}=\dfrac{l'}{l}=\dfrac{1}{31}\)

\(\Rightarrow\dfrac{T}{T'}=\sqrt{\dfrac{k'}{k}}=\sqrt{\dfrac{1}{31}}\Rightarrow T=\dfrac{2}{\sqrt{31}}\left(s\right)\)

Ban đầu: \(l_0;k_0\)

 \(\dfrac{W_t}{W}=\dfrac{\dfrac{1}{2}kx^2}{\dfrac{1}{2}kA^2}=\dfrac{64}{100}=\dfrac{16}{25}\Rightarrow W_t=\dfrac{16}{25}W\)

\(W_d=\dfrac{1}{2}mv^2=\dfrac{9}{25}W\)

Lúc sau: \(l=\dfrac{3}{4}l_0;k=\dfrac{4}{3}k_0\)

\(\Rightarrow W_t'=\dfrac{3}{4}W_t=\dfrac{3}{4}.\dfrac{16}{25}W=\dfrac{12}{25}W\)

\(W_d'=W_d\)

\(\Rightarrow W'=W_t'+W_d'=\dfrac{12}{25}W+\dfrac{9}{25}W=\dfrac{21}{25}W=\dfrac{21}{25}.\dfrac{1}{2}.18.0,1^2=0,0756J=75,6mJ\)

\(T_1=2\pi\sqrt{\dfrac{l_1}{g}};T_2=2\pi\sqrt{\dfrac{l_1\left[1+\alpha\left(t-t_0\right)\right]}{g}}\)

\(\Rightarrow\dfrac{T_1}{T_2}=\sqrt{\dfrac{l_1}{l_1\left[1+\alpha\left(t-t_0\right)\right]}}=\sqrt{\dfrac{1}{1+1,2.10^{-5}.25}}\Rightarrow T_2=\dfrac{9,8}{\sqrt{\dfrac{1}{1+1,2.25.10^{-5}}}}=...\left(s\right)\)

\(T_1=\dfrac{t}{20}\left(s\right);T_2=\dfrac{t}{30}\left(s\right)\)

\(\dfrac{T_1}{T_2}=\sqrt{\dfrac{l_1}{l_2}}\Leftrightarrow\dfrac{l_1}{l_2}=\left(\dfrac{T_1}{T_2}\right)^2=\dfrac{9}{4}\Leftrightarrow l_1-\dfrac{9}{4}l_2=0\)

\(l_1-l_2=5cm\Rightarrow\left\{{}\begin{matrix}l_1=9cm\\l_2=4cm\end{matrix}\right.\)

\(T_1=2\pi\sqrt{\dfrac{l_1}{g}};T_2=2\pi\sqrt{\dfrac{l_2}{g}}\)

\(\Rightarrow\dfrac{T_1}{T_2}=\sqrt{\dfrac{l_1}{l_2}}\Leftrightarrow\dfrac{l_1}{l_2}=\left(\dfrac{T_1}{T_2}\right)^2=\dfrac{1}{4}\)