A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed $\omega_2$. Length of different links are:

$$O_2=O_2A=L,$$

$$AB=O_4B=\sqrt{2}L$$.

The magnitude of the angular speed of the output link $4$ is $\omega_4$ at the instant when link $2$ makes an angle of $90^{\circ}$ with $O_2O_4$ as shown. The ratio $\frac{\omega_4}{\omega_2}$ is _____ (round off to two decimal places).