Firstly check you have followed the documentation for fine tuning apache2 and mysql:
http://library.linode.com/troubleshooting/memory-networking
Secondly, if this is as regular as clockwork - then something in cron will be the cause (logrotate on very large log files can cause thrashing).
Check your log files - if you have set anything to 'debug' and are no - longer debugging, switch it off.
Check the space you have available in your root... even Linux needs to breathe.
Sometimes these problems are hard to track - so monitor your node using:
iotop - disk usage per process
iftop - network usage per process (possibly not needed for your problem but useful to have handy)
top - general CPU and mem usage monitoring
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