Equilibrium everywhere

Classical Mechanics Level pending

A uniform rod of length \(L \) is in vertical plane with upper end resting against a smooth vertical wall \(OY\) (\(O\) being origin) and lower end resting on smooth surface \(OC\) which is perpendicular to the plane of the figure. Rod is in equilibrium for any position. If the equation of the curve \(OC\) is \(x^2+\omega y^2 + kLy =0\). Find \(\omega^2-k^2 \)+4.

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