Hamlet behaves abnormally with Ophelia, grabbing her wrist and stroking her face without speaking, and then walking out the door while facing her. He was also unkempt, and looked bewildered. He acts this way towards Ophelia, I believe, because she will inform others, such as Polonius, of his behavior. I believe that Hamlet's goal here is to get as many people as possible to believe that he is going out of his mind, so that they will not suspect that he is trying to exact revenge on Claudius for killing his father.
With Polonius, Hamlet acts completely obnoxious and immaturely makes fun of him. I believe that he suspects that Polonius was sent to watch his behavior, thus he acts erratically to throw Polonius off, which will in turn throw off Claudius. His behavior allows him to speak openly and gives him an excuse to act out, which I trust that he will do in later acts to avenge his father's death and get away with it. I suspect that Hamlet has a plan already, and that this madness is carefully calculated.
Excellent job on these!
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