96 V6 Shaking - Wrong Tires?

Hey everyone. Just bought a 96 Mustang with the V6.

It shakes when it hits 55 until about 65 or so. I'm thinking its because of the low-profile tires. Going to throw on a new set of tires and get an alignment tomorrow. Pretty sure this will take care of the problem.

Any insights or suggestions?
 
Check the driveshaft bolts. My car had a vibration after 45 mph when I took the load off the drivetrain. Got under there, and noticed that 2 of my 4 DS bolts were backing out...
 
Follow up:

Tried to have the tires rebalanced at four different places today. Everyone kept telling me they didn't have the machine to balance my after market rims. Finally, Tire Discounters was able to balance them, but I just elected to throw on 4 different tires.

The thing I didn't see before (since I bought the car at 11 o'clock at night without the best vision) was that the tires were pretty bald.

Anyway, car no longer shakes and was able to take it the rest of the 150 miles home hitting about 85 on the freeway with issue.

Still needs aligned though, pulls really hard to the right whenever I come to a stop.
 
I had this same problem for the last few months. Same speeds and everything. Just this morning I went to Discount Tires and had to completely replace my tires, now all is smooth sailing. Take your car to a tire shop, and have them look at them. There is a good chance that your problem lies therein. Good luck!
 
There is a TSB out for vibration at highway speeds. Ive done all the listed repairs (stiffer engine mounts, new struts, wheel rotate & Balance) except for the sub frame stiffeners. Not sure if I want to install those roadkill catchers under my car? Still have a vibration around 65 - 68. Just keep it above that and all is fine! Tire pressure seems to pay a role with it to.

Here is a list of TSB's and recalls.
Ford Mustang | The Center for Autosafety

Trying to find what the TSB says without having to pay may take some digging.
 
There is a TSB out for vibration at highway speeds. Ive done all the listed repairs (stiffer engine mounts, new struts, wheel rotate & Balance) except for the sub frame stiffeners. Not sure if I want to install those roadkill catchers under my car? Still have a vibration around 65 - 68. Just keep it above that and all is fine! Tire pressure seems to pay a role with it to.

Here is a list of TSB's and recalls.
Ford Mustang | The Center for Autosafety

Trying to find what the TSB says without having to pay may take some digging.

if you have the TSB number you can go into a ford dealer and ask for a copy of it. just FYI, the problem with TSBs listed on the internet is they can be incomplete or be obsolete.