\(\sum\omega=\sqrt{\frac{k}{m_1+m_2}}=\frac{2\pi}{0,5}=4\pi\Rightarrow\frac{k}{m_1+m_2}=160\Rightarrow m_1+m_2=\frac{k}{160}\left(kg\right)\left(1\right)\)
\(\omega_1=\sqrt{\frac{k}{m_1}}=\frac{2\pi}{0,4}=5\pi\Rightarrow\frac{k}{m_1}=250\Rightarrow m_1=\frac{1}{250}k\) (2)
\(\left(1\right),\left(2\right)\Rightarrow\frac{k}{250}+0,225=\frac{k}{160}\Rightarrow k=100\left(N/m\right)\)
\(\Rightarrow m_1=\frac{k}{250}=\frac{100}{250}=0,4\left(kg\right)\)