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A particle of mass m in xy plane is attracted toward the origin with the force

$$\begin{align}\vec{f} = - \frac{k^{2} m}{r^{6}}\vec{r}\end{align}$$ where ##\vec r## is position vector of particle measured from origin. If it starts at position ##(a,0)## with speed $$v=\frac{k}{\sqrt{2} a^{2}}$$ perpendicular to x axis show that trajectory of given particle is

$$\vec r= a cosΘ $$

The equation I got is Binet equation which I can't solve for r. Thanks for help

The Binet equation I got is:

$$\ddot r - \vec r w^2 = \vec f$$

Here f is same as (##1##)

$$\begin{align}\vec{f} = - \frac{k^{2} m}{r^{6}}\vec{r}\end{align}$$ where ##\vec r## is position vector of particle measured from origin. If it starts at position ##(a,0)## with speed $$v=\frac{k}{\sqrt{2} a^{2}}$$ perpendicular to x axis show that trajectory of given particle is

$$\vec r= a cosΘ $$

The equation I got is Binet equation which I can't solve for r. Thanks for help

The Binet equation I got is:

$$\ddot r - \vec r w^2 = \vec f$$

Here f is same as (##1##)

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