While I wouldn't say that I have problems sleeping as such, I certainly have problems waking up! My body clock never seems to really set itself into a good rhythm and I nearly always wake up feeling tired, so this little gem of a website, sleepyti.me is a bit of a saviour for me!
If you don't already know, we sleep in cycles. I remember learning all about this when I studied psychology, and essentially, these cycles consist of us moving from a state of light sleep into a deep sleep and back again, several times throughout the night. Each cycle will typically last around 90 minutes.
The most natural time for your body to wake up is in between cycles. If your alarm starts to sound while you're in a deep sleep, you will either sleep through it, or wake with a shock, feeling rather groggy.
Sleepyti.me calculates for you, at what time you should go to bed if you want to wake up bright-eyed and bushy-tailed, at the best point of your sleep cycle. It can also calculate for you the best time for you to wake up if you are already on your way to the land of nod. To be honest, it uses very simple maths, but when you're feeling a bit dozy, it's always nicer for someone else to do the brain work for you, right?
I hope you find this as helpful as I have.