It is correct but it isn't a sentence so it depends on how you intend to finish it. e.g. I used to have trouble sleeping. Whenever I woke up at about 4 o'clock in the morning, I would just get up and play computer games until it was time to go to work.

"whenever I woke up at about 4 o'clock in the morning~~" ( 4AM ) Is it right sentence? --> yeah it's not wrong but it's quite long. So make it shorter :)