When transmission is shifted into drive the RPM's drop and the car shakes

Hello,

In the diagrams down below I have included a possible list of things that could be causing the problem. So let's start at the top and inspect the air intake tract up to the throttle body and make sure that the air filter doesn't need to be changed. Please get back to us with what you find out and we can go from there, if needed.

Thanks,
Alex
2CarPros

The issue that I see over and over again with these trucks is the front engine mount failure that causes excessive engine vibration at idle in gear. I attached a picture of the mount in question. The instructions have you use an engine support brace, but the easier way is to use a floor jack with a wood block to support the engine from underneath. Just jack up the engine 25mm or so then you can remove the nuts and bolts in the picture to remove and replace the mount. You can verify that the issue is the mount by using a long pry bar and pry against the engine mount bracket to lift the engine away from the mount. If the vibration decreases then you will need to replace the mount.