Writing a CPU/RAM usage log over a period of time to file on CentOS

The standard ps is enough.

while true; do ps o pcpu,rsz -p $pid | tail -n1 >>usage.log; sleep $interval; done

result:

0.0  3352
0.3 31640
0.4 36924
0.5 36052
...

First field is CPU usage in %, second is physical memory usage in kbytes.

If you care about precise timing and want CPU in percentage:

watch --precise -n 1 'top -b -n 1 -p [PID] | tail -n 1 | awk "{print \$9}" >> [PID].log'