Solve for \(t_{\max }\) in Equation 3.17 in general for arbitrary variables. Then evaluate \(t_{\max }\) numerically for the cases in Table 3.1. Plot each case and discuss trends.

Table 3.1: Cases for tmax in Problem 9. Case (0) (in) (0) (in/s) w (rad/s) 1 2 0 5 0.1 2 5 0 0.1 2 3 5 5 0.1 2 4 5 5 0.5 2 5 5 5 1.1 2 6 5 7 5 5 0.1 4 5 0.1 10