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Learning Goal: I’m working on a aerospace engineering question and need the explanation and answer to help me learn.

A particle P of mass m=3.5kg arrives at point O with a horizontal velocity v0 and starts rolling down a circle with radius R=4m. The particle is attached to the point O by means of a linear spring of stiffness k=75N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N={n^x,n^y} be a fixed reference frame as shown in the figure and let B={b^x,b^y} be a reference frame attached to P so that b^x is tangent to the circular path and b^y is perpendicular to the circular path. For convenience, take g=10m/s2 in this question.