If your car is shaking only when you get to 60 MPH then it's likely that your tires are either out of round or unbalanced.
I would take the car to a tire shop or a mechanic and get the car checked out.
If your tires are out of round they can cause the car to shake when you get above 55 MPH and you can sometimes see if the tire is out of round or has a bulge in it by looking at the tires and running your hand over the tire to feel for out of round spots.
A tire shop can also look the tires over and if they are in good shape you can have the tires balanced again for cheap.
Warped brake rotors or even a bent rim can also cause a car to shake when you get to 55 MPH or higher.
I would have a mechanic or a tire shop take a look at the tires or vehicle to find out what is actually causing the problem.
Some tire shops will examine the tires for free or a small charge and can tell you if the tires are bad or the rims could be bent.