what pro told me was very simple: centre of the racket, there's where it's best. i believe it's what pros practically do. so i just follow, it's the easiest.

what scientists told me was very complex http://www.physics.usyd.edu.au/~cross/tennis.html : there are more than one sweetspot. the spots on a racket are (the analysis is on a tennis racket but i think it applies to badminton racket to a great deal):

1. vibration node. near the centre of the frame. this is where the racket gets the least vibration.
2. centre of percussion (COP). below the vibration node. this is where your hand/wrist/forearm get the least impact.
3. greatest bounce. below the COP. this is where the ball/birdie gets the most bounce power.

and there is a dead spot. above the centre of the frame. this is where the racket absorbs most energy of the ball.

so, hit birds with the mid- and bottom part of the frame, there are a string of goodspots out there. you'll hit one of them.