Why 2002 Hyundai Sonata shakes when brake applied.

SOURCE: 2006 Hyundai Sonata brake light problem

there is a tsb for the brake switch in 06 sonatas. it must be adjusted or replaced by dealership. is your check engine light on, if so its probably code p0504

SOURCE: Shake in steering wheel

I believe you need your disk brake rotors turned to be true again or have them replaced. Whe you use your brakes a lot and kit puddles of cold water then it will warp the rotors which will cause the violent shaking. You may not feel it in the brake pedal even if it is warped rotors. If you don't think you have warped rotors then you should be very careful driving it because it will probably be in the steering sector arm or the idler arm on the steering shaft.
Dale

SOURCE: Headlight bulb replacement for 2002 Hyundai

http://www.autozone.com/autozone/repairinfo/common/repairInfoMain.jsp?targetPage=productsHowToInspect&leftNavPage=productsHowTo&pageId=%090900c15280213e7e&subtitle=replace

SOURCE: hyundai sonata 2002 remote

There is a special (proprietary) programming electronics 'black box' for the keyless entry system on all Hyundai vehicles for programming the remotes. This programming is stored in either the BCM (body control module) or the ETACS module (Electronic Time and Control System).

SOURCE: My alarm on my 2002 Hyundai Sonata keeps going off

Experience with this problem points to several possible causes. First, hood switch is improperly adjusted or rubber button on the underside of the hood which strikes this switch is missing or worn out (does the 'answer back' feature (horn toot) occur when you press the "lock" button on the keyless remote twice?). If it doesn't, this is the first place to look -- is the hood bent out of shape? Often I have found the hood adjustment is SO CLOSE to the hood switch being 'CLOSED', that a simple gust of WIND can set off the alarm.
Next, each door and the trunk have switches which must be in their proper positions (closed -- Open Circuit communication with the ETACS module) for the burglar alarm to SET Active/ON. The problem could be at any one of these switches, not to mention the ETACS module itself. Best solution:Take/tow the vehicle into a Hyundai Service Center (dealership), pay the diagnostic fee. They will tell you EXACTLY what the problem is and what's needed to fix it (parts, labor, tax, time-frame, etc.).