Car vibrates in 2nd gear

Vehicle: 1999 BMW 323i, 120,000kms

Hello,

My car vibrates violently when accelerating in 2nd gear..

- This only happens when accelerating quickly in 2nd gear, and only from ~3,500rpm upwards.
- If I accelerate slowly in second gear, I can redline it without the vibrating occuring
- I dont get vibrations in any other gear
- It doesn't appear correlated to speed, as I can push 1st gear to 60 kmph and slip it straight into 3rd without any problem.

Any idea what the problem is?

Thank-you in advance!