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I am pretty sure that fixing both the velocity and the position to specific values does not work, because it would not conserve "energy".


Since we're not solving a PDE here, it's pretty easy to prescribe arbitrary values and derivatives at the boundary points and find an interpolating function---in fact, that's exactly what we did with cubic spline interpolation in Assignment 4. However, once we actually need to satisfy some additional criteria on the interior, we need to be more careful (as the next few slides reveal).