Small Engines (Lawn Mowers, etc.): what charges the batery, stators, charging systems

Question
I have a troy bilt year 2003 model number 13AN693G118 Serial number 1A133B30027 with a B/S number 31C707  0154E1  021003ZE I have charged the battery and will start I let it run for about 30 or 40 minutes and shut it off. would not start with out a jump the battery is a 235 cranking power it was tested and still had 200 cranking power. is that enough to do the job? How does the battery get charged and what ever it is does it go bad?  Thank you any helkp you can give  Gary

Answer
Here is a link that describes the charging system:

http://www.briggsandstratton.com/engines/support/frequently-asked-questions/~/me...

Briggs charging systems are pretty reliable.  Once in a while the diode/retectfire or regualtor will fail but the stators are very reliable.

Do you have a multimeter to check the charging system?

Eric