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Car shakes

vehicle shakes when driving between 58 and 62 mph. what could be wrong? seems to be from passenger side front.

The problem is most likely to be simply a case of a tire that needs to be rebalanced.

If that does not cure the problem, then you need to have a competent mechanic check the condition of front-end components such as ball joints and tie rod ends. Since worn/damaged front-end components are a major safety hazard, you should go to this next step right away if rebalancing the tire(s) does not do the trick.

I agree, a front tire is probably your problem, either a tire that is unbalanced because a weight has gone missing, or just because one or both front tires are worn. Specific speed viabration generally means tire wear.
Check the treads, pressure and sidewalls of your tires (look for fine cracks on the sidewalls). If all four tires are in reasonably good shape, have them rotated and balanced. I’d rotate front to back and vice-versa if all of the tires look okay.
My first guess is that your front tires are just worn, but how they are worn can help you diagnose if there is any other problem aside from simple wear. You can and should inspect your own tires for unusual wear before you buy new tires or decide on a repair of your front end. Here’s a pretty good site to help you