you have bubbles in the tires you need to get a wheel balance 1st and 2nd wheel allignment if it still plays up or the engine is loose / old = more expsensive
because of u <<not part of my answer>> Probably need to check/do an allignment.
allignment
The moment of inertia of the balance wheel about its shaft depends on the shape and distribution of mass in the wheel. To calculate it, you would need to know the mass distribution and shape of the balance wheel.
What make the steering wheel shake is the tires that need wheel balance.
Maybe needs front end allignment. I had that exact issue and it turned out to be the tie-rod ends.
wheel vibration at speed
check your allignment.
yes to balance well
you need the allignment doing if it is pulling to one side
no , changing front shock absorbers does not change any of the allignment settings so , if the wheels are PROPERLY ALIGNED before the shocks are changed , a wheel allignment would not be needed
That is static balance, basic, but not as important as dynamic balance.