| 1. 1 $F=-m\ddot y$ | 0.30 |
|
| 1. 2 $m\ddot x=-kx+mg-m\ddot y$ | 0.30 |
|
| 1. 3 $\rho sl\ddot y=-2\rho sgy+kx$ | 0.30 |
|
| 1. 4 $x_0=\cfrac{mg}{k}$ | 0.30 |
|
| 1. 5 $y_0=\cfrac{kx_0}{2\rho gs}=\cfrac{m}{2\rho s}$ | 0.30 |
|
| 1. 6 $x=x_0+A\cos\omega t$ | 0.30 |
|
| 1. 7 $y=y_0+B\cos\omega t$ | 0.30 |
|
| 1. 8 $A(\omega_1^2-\omega)=B\omega^2$ | 0.20 |
|
| 1. 9 $A\omega_3^2=B(\omega_2^2-\omega^2)$ | 0.20 |
|
| 1. 10 $(\omega_1^2-\omega^2)(\omega_2^2-\omega^2)=\omega^2\omega_3^2$ | 0.40 |
|
| 1. 11 $$\omega_{1,2}^{2}=\frac{\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2} \pm \sqrt{\left(\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}\right)^{2}-4 \omega_{1}^{2} \omega_{2}^{2}}}{2}$$ | 0.30 |
|
| 1. 12 $$\omega_{1}=\sqrt{\frac{\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}-\sqrt{\left(\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}\right)^{2}-4 \omega_{1}^{2} \omega_{2}^{2}}}{2}}$$ | 0.20 |
|
| 1. 13 Численное значение $\omega_1=5.19~\text{с}^{-1}$ | 0.20 |
|
| 1. 14 $$\omega_{2}=\sqrt{\frac{\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}+\sqrt{\left(\omega_{1}^{2}+\omega_{2}^{2}+\omega_{3}^{2}\right)^{2}-4 \omega_{1}^{2} \omega_{2}^{2}}}{2}}$$ | 0.20 |
|
| 1. 15 Численное значение $\omega_2=12.07~\text{с}^{-1}$ | 0.20 |
|