67 Impala vibration while accelerating....Help....

I have a 67 impala sedan H/T with a 327.  Recently I have notice a strong shaking or vibration on accelerating from a stop.  I can't tell if it's coming from the front or the rear but it seems to stop once I hit about 15 mph.  Any suggestions on what I am looking for?  

check the rear suspension bushings... see if they are worn...  letting the rear end change angles.... this causes drive shaft to do weird things...

are the motor or transmission mounts broken?????     that model did have retrofit cables that attached to the exhaust manifold bolts that looped around the upper control arm shaft... to prevent the motor mounts from breaking..  

I am pretty sure that the motor mounts may be broke...I just got it from the original owner and it's all original.  The motor does seem to shake an awfull lot when at adile.  I just haven't dove that deep into it yet.  Any sugestions?  

Either they have the wrong balancer or flex plate on it or you have a broken motor mount.  
Professional hi-performance engine builder

Horsepower sells Engines and torque wins races.

The balancer could have also spun inside the counter wight. you will see the rubber ring all worn out. If so it needs to be replaced before it goes though something or shatters. The flex plat might be cracked or broken as well. if so replace it before the converter goes into you trans. Motor mounts mights might be broke as well.  

This may sound weird, but also check your tires, not the balancing of them but uneven wear can cause vibrations at low speeds. I worked in a tire shop for 5 years while going to college.  

Definately the motor mounts