Optimized Circular Motion
Third string has the longest path with optimized radii
                        
                        First String (R=100)
                    
                    
                        
                        Second String (R=80)
                    
                    
                        
                        Third String (R=60)
                    
                    
                        
                        Path Traces
                    
                String Controls
                            
                            First String
                        
                        
                            100
                            
                        
                    
                            
                            Second String
                        
                        
                            80
                            
                        
                    
                            
                            Third String
                        
                        
                            60
                            
                        
                    Path Controls
                            
                            Show Path 1
                        
                    
                            
                            Show Path 2
                        
                    
                            
                            Show Path 3
                        
                    Animation Controls
                            Speed:
                        
                        
                            5
                            
                        
                    Optimized Configuration
Optimal Radii for Longest Third Path:
• First String: Radius = 100
• Second String: Radius = 80
• Third String: Radius = 60
• Total distance from center to third point = 240
• This creates the largest circular path for the third point
For constant angular speed, the linear speed at the end of a string is proportional to its radius (v = ω × r).
To maximize the path length of the third point, we need to maximize the total radius from center to third point.
With these values, the third point travels the longest path while maintaining a visually pleasing proportion between strings.
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