Answer:
The maximum length during the motion is 
Explanation:
From the question we are told that 
            The mass  is  
             The vertical spring  length is  
             The unstretched  length is  
           The initial speed is 
           The new length of the spring 
The spring constant k is mathematically represented as 
                            
 
Where F is the force applied  
            y is the difference in weight which is   
The negative sign is because the displacement of the spring (i.e its extension occurs against the force F)
     Now  substituting values accordingly 
                     
                        
The  elastic potential energy is given as 
   where D is this the is the displacement  
Since Energy is conserved the total elastic potential energy would be
              
              
 
Substituting value accordingly 
                 
                 
                  
                 
So to obtain total length we would add the unstretched length 
  So we have 
                   