Both Claudius and Gertrude urge Hamlet to forget about his dead father and start enjoying life again. Claudius even says,
We pray you throw to earth This unprevailing woe, and think of us As of a father; for let the world take note You are the most immediate to our throne, And with no less nobility of love Than that which dearest father bears his son Do I impart toward you.
Gertrude, Hamlet's mother, tells him,
Good Hamlet, cast thy nighted color off, And let thine eye look like a friend on Denmark. Do not for ever with thy vailed lids Seek for thy noble father in the dust. Thou know'st 'tis common. All that lives must die, Passing through nature to eternity.
Both Claudius and Gertrude are being partly sincere and partly phony. What really troubles them is that Hamlet's grief reminds them painfully of their own guilty behavior. The audience does not yet know that Claudius murdered his brother, but they will remember Claudius advising his nephew that the death of a father isn't really such an important matter. At that time the audience might also suspect that Gertrude was an accessory in her husband's murder or that she feels bad about remarrying so soon after her husband's death. The audience realizes that Gertrude had a guilty conscience when she told her son to forget his father, as she apparently has done so easily.
Actually, neither Claudius nor Gertrude has forgotten King Hamlet. Claudius is eaten up with guilt over the crime he committed. He probably knew he would suffer remorse for a certain length of time after committing the ghastly murder, but hoped he would get over the bad feelings and try to atone by being a good king and drowning himself in liquor. Gertrude was not involved in her husband's death and doesn't suspect that her new husband had anything to do with it; however, she feels guilty because she knows it was immoral if not sinful to marry Claudius after her husband had only been dead for a few months. Both Hamlet's mother and his uncle wish young Hamlet would forget about his father and stop making them remember their own sins. Their advice to young Hamlet is hypocritical and self-interested. Their reasoning with him is specious. Hamlet is the only person in all of this scene who is behaving properly. The new king and his wife, along with all the courtiers who are present, are trying to act as if life is full of nothing but pleasure and delight. When Claudius asks Hamlet, "How is it that the clouds still hang on you?" he is suggesting that the whole world is full of warm sunshine, and that this is a time to eat, drink, and be merry, not a time for mourning. No doubt every character in this scene is dressed in bright new clothing--with the exception of Hamlet, who is wearing a black suit and a black cloak and must stand out as a symbol of gloom and doom.
Hamlet must sense that his uncle and his mother are being overly solicitous and phony with him. He can detect it in the tones of their voices. They "protest too much." They make him a little suspicious of their motives. He is not terribly reassured by being promised the kingship after Claudius's death.
After everybody else exits, Hamlet speaks these prophetic words:
It is not, nor it cannot come to, good. But break, my heart, for I must hold my tongue!