Normally if the shimmy occurs at around 50-60 mph, I would suspect a tire out of balance. However if the shimmy is constant, it may be a bent wheel, loose wheel, loose wheel bearing, or worn suspension parts. Have your tires rotated and balanced. At that time have them check for a bent wheel. Make sure when they install the wheels back on the car they are torqued to factory specs. Have them inspect your front suspension parts for damaged or worn parts. Can also be a defective tire. Look for bulges on the sidewall, or a tire that is wearing unevenly. Make sure the tires are aired up to the specifications listed on the driver's door post or in your owner's manual. No more no less.
Wobble, or Death Wobble as it's sometimes called, could come from several sources, generally all of which originate in your front suspension and steering components. This would include any or all of your four tires. A tie rod even slightly bent from an off road trip or hitting a pot hole can be the culprit as well as worn bushings at the sway bar or other components. Another source of wobble can be the result of even a minor suspension lift including the use of larger tires than recommended by the manufacturer.
I highly recommend that you take this to a professional shop that can measure and adjust your front end because if left as it is, well, they don't call it Death Wobble for nothing.
Warped Rotors on your Front Brakes. Have them turned or purchase new ones.
Does it happen either way you turn? And, does it feel like it's coming from your tires or somewhere else?
The 2004 Jeep Grand-Cherokee has 41.7 in. of front leg room.
The 2004 Jeep Grand-Cherokee has 56.5 in. of front hip room.
The 2012 Jeep Grand-Cherokee has 40.3 in. of front leg room.
The 2004 Jeep Grand-Cherokee has 39.7 in. of front head room.
The 2011 Jeep Grand-Cherokee has 58.6 in. of front shoulder room.
This is a self-exited vibration problem.
Front rotors could be warped. Replace
The 2009 Jeep Grand-Cherokee has 59.1 in. of front shoulder room.
The 2013 Jeep Grand-Cherokee has 57.0 in. of front hip room.
The 2007 Jeep Grand-Cherokee has 57.1 in. of front hip room.
The 2002 Jeep Grand-Cherokee has 39.5 in. of front head room.
The 2004 Jeep Grand-Cherokee has 58.9 in. of front shoulder room.
The 2002 Jeep Grand-Cherokee has 58.9 in. of front shoulder room.
The 2013 Jeep Grand-Cherokee has 39.9 in. of front head room.
The 2011 Jeep Grand-Cherokee has 57.0 in. of front hip room.
The 2010 Jeep Grand-Cherokee has 57.6 in. of front hip room.
The 2005 Jeep Grand-Cherokee has 59.1 in. of front shoulder room.