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A particle of mass m free to move in the...

A particle of mass `m` free to move in the `x - y` plane is subjected to a force whose components are `F_(x) = - kx` and `F_(y) = - ky`, where `k` is a constant. The particle is released when `t = 0` at the point `(2, 3)`. Prove that the subsequent motion is simple harmonic along the straight line `2y - 3x = 0`.

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