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A particle of mass \( m \) moves due to the force \( \mathbf{F}=-\alpha \mathrm{mr} \), where \( \alpha \) is a positive constant, \( r \) is the radius vector of the particle relative to the origin of coordinates. Find the trajectory of its motion if at the initial moment \( \mathbf{r}=\pi_{2} \mathbf{i} \) and the velocity, \( \mathbf{v}=v_{0} \mathbf{j} \), where \( \mathbf{i} \) and \( \mathbf{j} \) are the unit vectors of the \( x \) and \( y \) axes.
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