The next four weeks of the 2nd month bring little more sleepless nights for the parents but, it's worth as your baby starts recognizing you.
The baby learns the art of social smiles and you should also be encouraging that by talking to them. The baby talk generally would not make sense but that is how the baby is going to learn, don't feel any about these silly talks. It's only in the 5th week that the baby realizes that they have arms and legs attached, it's in the 5th week they start experimenting with them, you should help them by waving their hand over their head and body. They will be interested in the toys you give them but they don't have hand and eye coordination to reach for them. By this week the baby can be awake for 10 hours in a day, although all at once in a stretch and may not be during the day. This will indirectly require your more time and you better be prepared for that. The changes in your baby will continue and the growth rate will depend from baby to baby, but you must keep a track of the growth.
The neck muscles are getting stronger and stronger and he/she will lift her neck for brief periods and will also turn the head around more and more from side to side. You can help them a great deal in this by standing just out of their vision and then calling them. This week they are ready to get a grip on almost anything which comes within their reach the baby is fascinated by the existence of fingers and how they work. The sleeping pattern also changes this week; they will have longer stretches of sleep up to 4 hrs in a stretch and if you are lucky those can be at night also. As parents, you always have the option to develop the night time sleeping patterns by singing songs or massaging the baby. They would have now developed facial expressions to communicate if you are observing them closely you would be in a position to understand what are the meanings of different body parts like eyes, lips, and eyebrows.
By the time the baby is 7 weeks old, they start seeing colors, up till now they only have been looking at things in black and white. You can stimulate babies' sight by exposing them to bright color objects. Their abilities to make sound will also improve, you can easily notice will develop a lot more sounds and, you can encourage them by talking back. The playtime of the baby will increase more and will need your attention. They will be more expressive towards their likes and dislikes.
Now, the baby can fully recognize familiar faces and will be able to follow moving objects. The hand and eye coordination would have improved. Neck movement would have also improved and now will be in a position to raise the head by 45 degrees approximately. He will be able to recognize familiar voices and will start looking at the direction from where the voice comes.