What is the purpose of the rubber block attached to the strut of a Camry engine mount (dogbone)?

All reciprocating internal combustion engines have a frequency by which they VIBRATE. we..the driver do not want to be aware of or feel this vibration. Thus the engine is mounted in the engine bay by Motor Mounts. That Dog Bone is one of them. That little rubber block...of a certain MASS ....fine tunes the mount to cancel out the vibration at that point in the engine. I remember seeing such a block attached to the ...Transmission....the rear Axle....the Exhaust System...and even certain Power Steering systems.

Very informative...thanks. But is it adjustable, i.e., can it be moved and relocated along the strut as a means of "fine-tuning," or is its location engineered to stay put?

I do not think this rubber block is itself adjustable. However....IF...all the other Motor and Transmission Mounts are in good shape....we sometimes start ADDING WHEEL WEIGHTS on top of the Block and securing it with a worm clamp. We then check the Vibration with a special piece of equipment to check the Frequency of the Vib. The name of that equipment?????. When I think of its name ...I will post.

Reed Tachometer. Old School but very effective in locating a vibration issue and ..creating a counter vibration to correct an imbalance issue.