| $F=-m\ddot y$ | 0.30 |
| $m\ddot x=-kx+mg-m\ddot y$ | 0.30 |
| $\rho sl\ddot y=-2\rho sgy+kx$ | 0.30 |
| $x_0=\cfrac{mg}{k}$ | 0.30 |
| $y_0=\cfrac{kx_0}{2\rho gs}=\cfrac{m}{2\rho s}$ | 0.30 |
| $x=x_0+A\cos\omega t$ | 0.30 |
| $y=y_0+B\cos\omega t$ | 0.30 |
| $A(\omega_1^2-\omega)=B\omega^2$ | 0.20 |
| $A\omega_3^2=B(\omega_2^2-\omega^2)$ | 0.20 |
| $(\omega_1^2-\omega^2)(\omega_2^2-\omega^2)=\omega^2\omega_3^2$ | 0.40 |
| $$\omega_{1,2}^{2}=\frac{\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2} \pm \sqrt{\left(\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}\right)^{2}-4 \omega_{1}^{2} \omega_{2}^{2}}}{2}$$ | 0.30 |
| $$\omega_{1}=\sqrt{\frac{\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}-\sqrt{\left(\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}\right)^{2}-4 \omega_{1}^{2} \omega_{2}^{2}}}{2}}$$ | 0.20 |
| Численное значение $\omega_1=5.19 \text{с}^{-1}$ | 0.20 |
| $$\omega_{2}=\sqrt{\frac{\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}+\sqrt{\left(\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}\right)^{2}-4 \omega_{1}^{2} \omega_{2}^{2}}}{2}}$$ | 0.20 |
| Численное значение $\omega_2=12.07 \text{с}^{-1}$ | 0.20 |