1) Driveshaft: Check the driveshaft for any imbalances, damage, or worn-out universal joints. A faulty driveshaft can cause vibrations at certain speeds.
2) Wheel Bearings: Worn-out or damaged wheel bearings can cause the wheels to wobble and vibrate, especially at higher speeds.
3) Steering Components: Inspect the steering rack, steering linkage, and tie rods for any looseness or damage. Worn-out steering components can cause vibrations in the steering wheel and the vehicle.
4) CV Joints: Check the Constant Velocity (CV) joints for any tears, cracks, or damage. Worn-out or damaged CV joints can cause vibrations, especially when turning or accelerating.
5) Engine Mounts: Inspect the engine mounts for any wear or damage. Worn-out engine mounts can allow excessive engine movement, which can cause vibrations.
6) Transmission Issues: If the vehicle shakes only when the transmission is engaged, there may be an issue with the transmission itself, such as a worn-out torque converter or transmission mount.
It's recommended to take your vehicle to a qualified mechanic for a thorough inspection to identify the exact cause of the shaking at 60 mph and have it repaired accordingly.