What would make a steering wheel shake between 50-70 km?

If your steering wheel shakes between 50-70 km, it probably has nothing to do with the steering wheel! It probably has something to do with the front wheels, alignment, or steering linkage. See if a front wheel has uneven wear. See if a piece of rubber is torn or perhaps missing. Take it to a place that sells tires and alignments. They will be able to spot the problem.

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If the vibration is confined to a certain speed range, the most likely cause is an unbalanced wheel. BTW, the units there should be km/h. Km alone is just distance, not speed.