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Why does the solution to pendulum problem with the geometric approach of Jacobi metric does not correspond to the solution with Lagrangian approach? [closed]

When we solve the pendulum problem with EL equation, we get to the differential equation $\ddot{q}+\frac{g}{l}\sin q=0$ but when I apply the substitution $t \rightarrow t\sqrt\frac{g}{l}$ and ...