If one of the four spark plugers or their wires does not work well,
your car will shake too. If your car has uphill shake (more load)
and no downhill shake, check your spark plugers and their wires.
If your car has uphill and downhill shakes, that can the problem
of tires.
First of all, what kind of car is it. Every car has a specific speed with virbration. If you can only feel the vibration at that speed, not below and over that speed, it should be fine. Try 120km in your case, if still feel it, check wheel balance.
why u do not listen to me?
My friend have same problem before.
My sugesstion: go to dealer and check transmission oil first to see if it need to be changed.
Sorry, I am not expert. I do not know why.
But I am sure it happend to my friend.
His car is 1989 camery, it shake when he drive on high way at 100km/h, but 80 is ok.
My another friend who know more about car suggest to change the transmisiion oil. It happend last year. now the car never shake again.
so I think he need check it if he did not chage for long time.