The tip of a rod vibrates so that its vertical position is

                      i (omega*t + phi)
          y(t)  =  A e

  where

                 A  =   5.2 m
             omega  =   0.3 rad/s
               phi  =  -3.2 rad


  
  Q:  At the time t = 5 seconds, what are the components
           of the complex vector representing the position
           of the tip of the rod?


            y(t = 5)  =  -0.67 m  -  i 5.16 m



  Q:  How long will it take from this moment (t = 5 s) until the rod
           reaches its maximum height?


             max y value is when  y = A = 5.2 m

             requires   cos(omega*t + phi)  =   1

                           (omega*t + phi)  =   0   or  2 pi  or  4 pi ...

             Try using value of 0.

                         (0.12 m/s)*t - 3.2 rad  =  0

                                 0 - (-3.2 rad) 
                          t  =  ---------------  =  10.67 s
                                    0.12 m/s


             So, if time is currently t = 5 s, 

 
                     --->  we must wait 5.67 s for tip to reach max height