Manual or automatic?
Tough to say what it could be.
60mph means alot of rotation from tires, if a balance weight came off or belt separated it could act that way.
Belt separation can cause a tire to vibrate only at a certain speed, below or above the speed it is smooth.
Drive line issue, maybe rear differential, long shot would be u-joints, but they tend to "clunk".
If automatic it could be torque converter lock up is acting up, computer controls that and gas pedal position is used by the computer
Last edited by RonD; 04-27-2016 at 09:44 AM.