Based on the short initial scene of Act IV, is it unclear if Gertrude truly believes Hamlet is mad or not. What it is clear is that the Queen seems to be more allied to her King than her own son. After her encounter with Hamlet which ends with Polonius' death, Gertrude does not hesitate to tell King Claudius what her son has done, yet she does keep her word by not telling him that Hamlet has just merely been faking madness. With her actions, the Queen has sealed Hamlets faith with the King who decides to send his to England. It should be mentioned that Gertrude still has no proof that Claudius is a killer and thus, if it is for her own benefit or not, she does not feel the need to protect Hamlet from him. On the other, the Queen could have interpreted her son's rash actions against her, sighting of the ghost, and murder of Polonius as Hamlet being insane.
2. Ophelia's madness is caused by her father's murder and his quick burial. When speaking to the Queen, Ophelia states "He is dead and gone, lady, He is dead and gone, At his head a grass-green turf, At his heels a stone." undoubtedly referring to her father's passing. She is so full of despair and sadness that she "cannot choose but weep, to think they should lay him i' th' cold ground." Ophelia speaks in rhymes and songs, which depicts how the death of her father has caused her to go mad. Another possible cause for Ophelia's madness is her trust and love for Hamlet which is not returned by him. Circumstances such as Hamlets unrequited love and his exile, her fathers death and Laertes being far away, come together to drive Ophelia into loneliness and madness.
3. Shakespeare differently portrays Hamlet's feigned madness and Ophelia's real madness in various ways. One way is that Shakespeare has Hamlets character announce feigned madness before he commences his acting while Ophelia suddenly is portrayed insane. Hamlet therefore is faking his insanity whereas Ophelia is not.