Given the above graph, I have to find the relation between $u_i$ and $\phi$. I need insight on how to relate these two graphs and come to the derivation as shown below: derivation
2026-05-06 08:54:05.1778057645
Finding function from the graph
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The three discontinuous $-u_i$ regions (slopes are zero, positive, zero, negative,zero ) are integrated with respect to time getting continuous function $\varPhi$ but with discontinuous slope/rate jumps as shown.