Rotation and Elongation of a spring 1

A very long thin tube is hinged at a point such that its free to rotate in the horizontal plane. Inside the tube there is spring fixed at its end. the spring is connected to a mass \(m\) which precisely fits into the tube.

At the instant \(t=0\) when the spring is in its natural length of \(R\), the mass is given velocity \(V\) in a direction perpendicular to the length of the tube.

If the maximum elongation produced in the spring is \(X\) then find the value of \( (100X^2 + 99)(X+2) \).

In this case, \(m = 2 \text{ kg}, V = 1 \text{ m/s}, k = 200 \text{ N/m}, R = 1 \text{ m} \).

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