A Problem from my book -2

Classical Mechanics Level pending

A mass of \( 2 \text{ kg}\) is attached to a spring of spring constant \(k\). The system can rotate about point \(O\). The system is initially at equilibrium and arrangement is vertical. The block is given a velocity \(v\) minimum so that it just(boundary condition) completes its one revolution around point \(O\). Find the eccentricity of path followed by the block about point \(O\). ( \(g= 10 \text{ m/s}^2\))

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