did this start all of a sudden? have you changed anything... ie, rotated tires, went wheelin, hit a pot-hole? Something had to spark it.
You say that it starts shaking in between 2nd and 3rd, does that mean while no gears are engaged? The vibes here and the vibes at 60 could be 2 different things. I would bet that the 60mph vibes are some tire issue. The other is weird and we need more info. Where do you feel the shake? steering wheel? seat? stick shift?
Other than balancing the wheels, check the motor and transmission mounts. That be my second suspect.
C