A particle of mass M is free to move in the horizontal plane(xy-planne here). It is subjected to force [itex]\vec F = -k\left(x\hat i + y\hat j\right)[/itex], where 'k' is a positive constant.(adsbygoogle = window.adsbygoogle || []).push({});

There are two questions that have been asked here:

1] Find the potential energy of the particle.

[tex]\vec \nabla \times \vec F = 0[/tex]

The given force is conservative and hence a potential energy function exists.

Let it be U.

[tex]F_x = -\frac{\partial U}{\partial x} = -kx[/tex]

[tex]F_y = -\frac{\partial U}{\partial y} = -ky[/tex]

[tex]U(x,y) = \frac{k}{2}\left(x^2 + y^2) + C[/tex]

2]If the particle never passes through the origin, what is the nature of the orbit of the particle?

I am not sure what the PE function tells about the trajectory of the particle. Explanation needed...

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# PE function

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