Thanks a lot
How can u prove this ?
Only for very large values of x, can the rate of change of radial speed be ignored
But u just put the value of k which u gave by assumption that rate of radial speed is non zero . that's why u got that condition. Can u prove from initial conditions (not by k ) ? @Maheshsai_Mudduluru
It hasn't been assumed anywhere that the rate of change of radial speed is non-zero at the point of maximum elongation. It's just a result of the case.
The value of k obtained here is the General expression for all values of x. As x approaches infinity, the rate of change of radial speed will be zero. In this case, the expression of k will approach that value obtained for which the radius of curvature is taken to be l+x.
For all practical cases, as x tends to infinity, the linear spring force relation is not satisfied. So if there is an ideal spring which satisfies the linear spring force relations, for such springs the case when x tends to infinity can be seen.