Can shake back wheel side to side when bikes not moving

Hi I suppose it can only be the headstock bearings are loose/worn. Taper roller bearings are the way to go but if already fitted loosen lock nut tighten cone until tight & then back off same until forks turn freely from side to side.
If problem not resolved then defo new bearings or possibility fork slider bushes are worn if high mileage bike.

First check the tire-pressure, then the fork oil; see if the wheel has a loose bearing play.

Speed Wobble - When The Bike Shakes Its Head - Cycling ...

cyclingtips.com.au/2011/.../speed-wobble-when-the-bike-shakes-its-head...

Speed wobble is the term used to describe a quick oscillation of the handlebars ... 2 A scenario seen relatively often is that the top tube of the bike is under-built.

Road Bike High Speed Wobble 1st person view ( Shimmy ...

? 1:27
www.youtube.com/watch?v=hMNFS2ap3fU

Jun 23, 2014 - Uploaded by Aurimas Petraitis
Road Bike High Speed Wobble 1st person view ( Shimmy ) .... causing my bike to be so twitchy on descents ...

Sounds like loose 'cones' in the rear wheel hub. The cones are cone-shaped nuts that the bearings run against, being held in place within the hub in the 'cup' of the hub. Tighten the cones until there is free rotation of the wheel with no lateral play. Hold the cone in place with the spanner whilst tightening the lock-nut and recheck the adjustment. If you lack the tools take it to your nearest independent local bike shop and they will surely be happy to help.

Could be a bad tire ( or bent rim Have balance checked), ball joint, idler arm, wheel bearing, steering tie rod end or defective rack and pinion unit. Lift vehicle about 1 inch off ground ( do each side independently) Use a pry bar and pry from ground up and down on wheel. Much play? bad ball joint. With both hands, try to move wheel side to side. Much play? could be a tie rod end or bad wheel bearing. Visually check play of steering arm into rack and pinion unit, more than about a half inch play, bad rack and pinion unit. Try to move back and forth with hands top and bottom. Much play? Bad ball joint or wheel bearing, verify visually that it is ball joint moving, else it is the wheel bearing. Manually check for play in each joint in steering control rods from steering knuckle all the way through each rod where there is a joint. Replace the one you find excessive play in. Check mounting studs for sway bar for loose fit, deteriorated rubber bushings or a crack / break in the sway bar. Replace if needed. That's about all I can think of unless it only happens when applying brakes, in which case it could be a warped rotor.

Sounds like a broken tie rod...do not attempt to drive

The most common cause would be tie rod ends. Watch them closely as you move the wheel back and forth. It may be the outer one next to the wheel or the inner one next to the engine. It's also possible your control arm bushings are the culprit. If so you should be able to see movement in the control arm itself when you move the wheel. Chech bot5h top and bottm control arms.

You will need either an adjustable wrench, a socket of the right size, or a box end wrench of the right size
(If you read through this and still don't feel like you're up for it, your local bike shop will be more than happy to do it - and it will either be really cheap or free)
The bolt you need to loosen is on the back wheel where the training wheel meets the bike. Find the right size tool for the job.
Grab the back wheel and try to wobble it side to side, then remember how much give there is so your end result gives the same feel.
You may need a second wrench to place on the nut/s between the frame and the hub to prevent this from turning, though it will probably only be needed for tightening everything after you're done.
-Start on 1 side (doesn't matter which one) and loosen the outside bolt with your wrench/socket
You will need to remove it completely to take the training wheel off of that side.
-Slide training wheel off and hand-thread the bolt back on, not tight yet.
-Do the same for the other side, both training wheels should be removed at this point.
It may help to have someone else for this next part
-Pull the back wheel as far back as it will go, don't kill yourself, but make sure the chain won't slip off because it's too lose. Make sure the wheel is aligned with the bike frame, not twisted, otherwise it will loosen on its own
-Tighten one bolt on the outside down onto the frame. This is where you might need to use a second wrench to keep the hub from rotating. Don't turn the nuts on the axle in the area inside the frame (between the frame and the wheel) as they should be tightened correctly, instead just hold them steady while you tighten the outside nut onto the frame. If that wasn't clear, you're pinching the frame between the nuts inside, which you never moved, and the nut outside the frame, which you removed to take the training wheel off.
-Repeat for the other side while still maintaining tension on the chain.
-You should be done, check to see if the wheel can wobble side to side and compare to your earlier result. If it moves too much, continue tightening outside bolts (both sides until they're good and tight)

This happens when the back wheel is not aligned properly with the chain. As the wheel turns the chain is being pulled to one side causing it to slip to the next set of cogs. To solve the problem first you need to loosen the wheel by opening the 2 nuts on the axel. If the chain slips inwards towards the wheel you need to move the front part of the back wheel to the left from a view point behind the bike. If it slips outwards away from the wheel then you need to move the front of the back wheel to the right as viewed from behind the bike. When the chain and cogs of the rear wheel are lined up in a straight line the problem should be solved.

When you go to lock it or unlock the steering give the bars a little wiggle while turning the key. Somtime the rod that goes into the hole gets gummed up. As for the front end wobble I would take a look at the wheel to see if it has gotten bent or if you have lost a wheel weight. Also check the wheel bearings buy getting the front wheel off the ground and hold the front end from moving and grab the top and bottom of the wheel and see if there is any side to side rocking movment. If there is stop riding the bike and get them replaced.

It could be an indication of a bad wheel bearing assembly. Did you check the lug nuts to be sure they are tight? It could also be the tie rod assembly. I would take off the wheel and try to move the just the hub assembly. Do you hear any screeching/squealing noises? Any popping while you are driving? Are your tires wearing? All these are classic signs of a bad wheel bearing. Any decent tire/auto shop can put your car on a lift and check the wheel bearings.