Hi Keith, and welcome to the gang!
The guys have made suggestions for all the MOST LIKELY causes for wobble. There's more, but they covered 'em...
But a little 'why' might help you find an elusive gremlin:
The basic geometry and physics of a motorcycle rolling in a straight line, is a balance between stability, and responsiveness. Look at the front wheel of a shopping cart when it rolls, and you'll see that the wheel always tries to point in the direction the shopping cart is going... it does this, because the wheel's axle is on a pivot, but is not centered beneath the pivot... it's offset. When the cart moves, the caster turns 'till the axle BEHIND the pivot, so the wheel's axis TRAILS the rotation.
Some shopping carts roll nice, but some have a wheel that flippy-flaps all over as you tour the Fresh Produce. it's doing this, because the wheel can't find a nice way to roll straight.
Grab a pop can, and a red plastic cup. Set 'em both on a flat table. Give the pop can a push... it'll roll straight. Do the same with your red plastic up... it turns in circles. Why? Because the diameter of the pop can is same on left AND right sides. The plastic cup, however, is smaller at the bottom, and larger at the top. In order to roll, the TOP edge needs to travel farther than the bottom. In order to roll a straight line, that plastic cup would need to be rolling JUST on it's TOP rim, not the side... because rolling on it's side would inherently pull it to right, or left.
Now look at a motorcycle from the side. Imagine that the forks come out of the frame, and went STRAIGHT DOWN... like a kid's tricycle. It'll steer, but you'll have a heckuva time balancing it (twitchy!!!) and it would NOT be safe to 'let go' of the bars, as that wheel will flop any-which-way at the slightest bump. Now reposition the wheel axle was 5" BEHIND the fork tubes. Yeah, it'd look stupid, but that's the way a shopping cart wheel is configured, right?
It would still be 'twitchy', NOT be easy to steer, or keep a motorcycle upright with that geometry, but with enough guts and strength, you could... it would want to go in whatever direction the motorcycle was travelling, but you could let go of the bars, and it would steer in the direction you're rolling... because you have TRAIL. More trail, means more of a 'desire' for the wheel to want to turn towards the bike's direction.
Tilt the forks to what looks more like a 'motorcycle'... this is called 'Rake'... and it does SEVERAL things, but mostly, it reduces the amount of steering response, for a given amount of steering input. Reason... when there is no rake (vertical), five degrees of handlebar turn equates to exactly five degrees of wheel direction change... but with 45 degrees of rake, five degrees of handlebar, only change the direction of the front tire by a FRACTION of that (I'd say 2.5 degrees, because SIN45 is 0.5, but there's other factors coming that invalidate that)
Now it gets funky. Take out your imaginary chalk, and draw a line THROUGH THE AIR... down the center of the steering tube, to a point on the ground ahead of the motorcycle. Now mark a point where the front tire contacts the GROUND. You'll readily see that the tire is contacting the ground BEHIND the steering axis. Yep, that's trail. Even when the wheel's AXLE is mounted on the FRONT of the tubes, the CONTACT point is still BEHIND.
Crazy, no?
No... it works!
Back to dixie cups... No... let's talk about flat-belt drives.
In an old machine shop, there's lineshafts spinning overhead, and big wide flat leather or canvas belts whirling around, driving all sorts of evil-looking bangy-rattley tools. If you look CLOSELY, you'll see the big sheaves that those belts ride on, are NOT flat. They're actually 'crowned'...
They're taller in the middle, than on the sides... like... two dixie cups mouth-to-mouth.
Why? Because the radius of the center, being larger than the ENDS, makes the belt WANT to run IN THE MIDDLE... it helps keep the belt centered.
Now imagine that sheave wasn't a sheave, but a tire, and the belt wasn't a belt, but a smooth stretch'a highway. The highway obviously isn't gonna move to keep the TIRE centered, but the TIRE will WANT to roll on it's HIGHEST.
Why?
Back to dixie cups...
If you have two facing mouth-to-mouth, and you roll it along, one side will tip, and the cup will hook in THAT direction (because they roll in a circle, not straight, remember?
On the motorcycle, the TRAIL means the wheel will CASTER... it will TRY to point itself in the direction it's rolling... a sudden jerk to the right, will lean the tire to the SMALL radius of the tire, which will then steer the tire to the right, but be counteracted by the tire wanting to roll on the center (Crown) of the tire.
Now, there's a dozen detailed variables that'll cause goofy oscillation, but by FAR the most common, is anything that will affect the way that tire WANTS to roll. A front tire that looks like a pop can (totally flat tread) or a pair of dixie cups (a wedge) will be problematic... a tire with a nice, constant curve from side to center, will be much less skittish... and USUALLY, either tire pressure, or a worn-out tire will be the primary culprit.
Wheel bearings, steering tube bearings, fork sliders, fork seals, or fork springs... bad swingarm bushings... or a CRACKED AXLE SHAFT can cause 'em to be problematic. A worn REAR tire can too... albeit not quite as much as a worn front.
Another thing that can make them very skittish... having too much weight too far to the rear.
Put away the dixie cups, wipe the spiked cool-aid off the table, put away your notebooks, take out your pencils and paper, its time for a quiz...
