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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