360 motor in 1972 Dodge Demon vibrating

Is it an automatic? Like MoparMan1806 said, the torque converter is different for a 360, too. It has a large balance weight welded on. You can use a regular 904/727 torque converter, but only if you buy a weight and weld it on. Or, you can buy a special flex plate from B&M that looks like a metal frisbee with a semi-circular "bite" taken out of one edge. The bite accomplishes the same thing that a balance weight on the converter housing would. Both things (harmonic balancer +weighted torque converter or harmonic balancer + special flex plate) are needed for an automatic with a 360. If it's a manual...I don't know. But it wouldn't surprise me if something weird had to be done to the flywheel to make it work with an externally balanced engine like the 360.