\(T=\frac{2\pi}{\omega}\Rightarrow\omega=\frac{2\pi}{T}\)
\(\Rightarrow\omega_1=\sqrt{\frac{k}{m_1}}=\frac{2\pi}{0,6}\Leftrightarrow\frac{k}{m_1}=\frac{100\pi^2}{9}\Rightarrow m_1=\frac{9k}{1000}\)
\(\Rightarrow\omega_2=\sqrt{\frac{k}{m_2}}=\frac{2\pi}{0,8}\Leftrightarrow\frac{k}{m_2}=\frac{25}{4}\pi^2\Rightarrow m_2=\frac{4k}{25\pi^2}=\frac{4k}{250}\left(kg\right)\)
\(\Rightarrow\sum\omega=\sqrt{\frac{k}{m_1+m_2}}=\sqrt{\frac{k}{\frac{k}{40}}}=2\sqrt{10}=2\pi\left(rad/s\right)\)
\(\Rightarrow\sum T=\frac{2\pi}{\sum\omega}=\frac{2\pi}{2\pi}=1\left(s\right)\)