Is it me or the truck? Clutch/transmission question

[agnes the dog]

Hi,

I have had my truck for about 4 days now and have noticed that it shakes sometimes when taking off from a complete stop. It has the 3 on the tree with a 305 (not modified) V8. I notice when I give more gas and release the clutch the truck seems like it is going over a rough railroad track. Pushing the clutch again and releasing will stop the shake and the truck drives great. This only happens when taking off rather quickly. A rolling start doesn't cause the shake. I noticed that the shaking issue has been less frequent over the past few days, but it's still there. The PO said that the truck had been in storage for a long time and wasn't driven. The motor is strong and I don't suspect that it would cause this. I really don't know what rear end gear is in there. Is it my driving style or is there something that I should think about fixing or adjusting?

Thanks,

JJ