\({A_1} = 20{\rm{\;cm}};{A_2} = 10{\rm{\;cm}};{T_1} = {T_2} = 0,8{\rm{\;s}}\)

\( \Rightarrow {\omega _1} = {\omega _2} = 2,5\pi \left( {{\rm{rad}}/{\rm{s}}} \right);{\varphi _1} = - \frac{\pi }{2};{\varphi _2} = - \pi \).

\( \Rightarrow {x_1} = 20{\rm{cos}}\left( {2,5\pi t - \frac{\pi }{2}} \right)\left( {{\rm{cm}}} \right);{x_2} = 10{\rm{cos}}\left( {2,5\pi t - \pi } \right)\left( {{\rm{cm}}} \right)\).