Have you had the tires balanced and the wheels inspected for a bent wheel. Also have the tires themselves inspected for a defect. Can also be a worn CV joint or U-Joint in the drivetrain. Can also be a broken motor mount.
Yes if the shocks are bad it can allow a shake to happen It will also put a lot more stress on other things and cause them to wear out very fast Worn shocks can also allow tires to wear improperly so that they will shake also.
a bad bearing will cause it to shake, also a rotar or shocks will do the same.
if front wheel drive check cv axles.
Shocks and other suspension components (A-frame bushings, etc.) deserve a close inspection, and all connections (tie rods, etc.) should be checked.
needs tires balenced or new shocks(struts)somtimes both
If you change the suspension geometry (which you did if the shocks weren't the exact same size/grade/damping) then you might have to take it to a professional. There are just too many variables, like power steering, steering fluid, brake fluid, brake disks installed properly, ect. Go to someone who knows what they are doing is my suggestion.
Replace your steering dampner. Mine did the same thing.
One possible answer: Loose bolts in combination with bad shocks or struts.
Aside from the aforementioned imbalanced tire and alignment (which could be incorrect toe in, castor, or camber), worn/damaged steering components, worn shackle pins, faulty wheel bearings, and damaged rims are another possibility.
The legs may shake if the dog is frightened.
Make sure your rotor isn't warped and that your tires are properly balanced. Also look for a bent wheel or bad wheel bearing.
One of the shocks on that side is probably bad.