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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: $$O_2 O_4=O_2A=L,$$$$AB=O_4B=\sqrt{2}L$$

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).