Question: Smoothest force sequence to move a mass. We consider the same setup as the example given on page 343 of the textbook, where the 10 -vector \(f\) represents a sequence of forces applied to a unit mass over 10 1-second intervals. As in the example, we wish to find a force sequence \(f\) that achieves zero final velocity and final position one. In the example on page 343, we choose the smallest \(f\), as measured by its norm (squared). Here, though, we want the smoothest force sequence, i.e., the one that minimizes

(This is the sum of the squares of the differences, assuming that \(f_{0}=0\) and \(f_{11}=0\).) Explain how to find this force sequence. In the Julia portion of this homework, we will also plot this force sequence.

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