Ubuntu 12.04: Random freezes

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http://unix.stackexchange.com – I get random freezes with Ubuntu 12.04 (kernel 3.2.0-31). The entire system freezes, mouse pointer doesn't move, keyboard input doesn't work. I'd say this happens about once per week on a system that is up 24/7. A hard reboot solves the problem. My questions: (1) Has anyone else experienced this? (2) I have a suspicion that a kernel upgrade may solve this. How much of a pain in the ass is it to upgrade an Ubuntu kernel, and how much will I break things like apt-get if I do upgrade the kernel myself? (HowTos)