The following script prints time stamps and a header.

#!/bin/bash -e

echo "      date     time $(free -m | grep total | sed -E 's/^    (.*)/\1/g')"
while true; do
    echo "$(date '+%Y-%m-%d %H:%M:%S') $(free -m | grep Mem: | sed 's/Mem://g')"
    sleep 1
done

The output looks like this (tested on Ubuntu 15.04, 64-bit).

      date     time          total       used       free     shared    buffers     cached
2015-08-01 13:57:27          24002      13283      10718        522        693       2308
2015-08-01 13:57:28          24002      13321      10680        522        693       2308
2015-08-01 13:57:29          24002      13355      10646        522        693       2308
2015-08-01 13:57:30          24002      13353      10648        522        693       2308

Occasionally when the need arises I just do:

$ top -d 1 -b |grep <process> >>somefile

It's not an elegant solution, but gets the job done if you want the quick crude value to verify your hypothesis.

You can use the following command in bash like so:

for i in `seq 0 60`; do
  echo `cat /proc/meminfo | grep Active: | sed 's/Active: //g'` >> usage.txt
  sleep 1m
done

This command will record the current memory use to a file named 'usage.txt' every minute for the duration of 1 hour.

If you wish, you can change the usage.txt part of the command to save under a different name. You can also change the sleep 1m command to alter the time between each entry and the '60' in the seq section at the top to change the number of entries to be recorded.

When you have finished making your entries, you will have a text file of entries that can be imported into a spreadsheet for easy comparison.

EDIT: If you wish to also record the total memory with each entry, you can use the following commands:

for i in `seq 0 60`; do
  echo `cat /proc/meminfo | grep Active: | sed 's/Active: //g'`/`cat /proc/meminfo | grep MemTotal: | sed 's/MemTotal: //g'` >> usage.txt
  sleep 1m
done

These commands will instead record entries in the form of <active>/<total>

Technically, you can mount /var/log as tmpfs. You'd need to be sure that /var/log is mounted before syslogd starts, but that's the case by default on most distributions since they support /var on a separate partition.

You'll obviously lose all logs, which I guarantee will be a problem one day. Logs are there for a purpose — there're rarely needed, but they're there when they're needed. For example, if your system crashes, what was it doing before the crash? Since when has this package been incstalled? When did I print this document? etc.

You won't gain much disk space: logs don't take much space relative to a hard disk. Check how much space they use on your system; I'd expect something like 0.1% of the disk size.

You won't gain any performance. Logs amount to a negligible part of disk bandwidth on a normal desktop-type configuration.

The only gain would be to allow the disk to stay down, rather than spin up all the time to write new log entries. Spinning the disk down doesn't save much electricity if any: the hard disk is only a small part of a laptop power consumption, and spinning up requires a power surge. Furthermore spin cycles wear down the disk, so don't spin down too often. The main reason to spin down is the noise.

Rather than putting logs on tmpfs, arrange for your disk not to spin up when a file is written. Install Laptop Mode, which causes writes to disk to be suspended while the disk is spun down — only a full write buffer, an explicit sync or a disk read will spin the disk back up.

Depending on your configuration, you may need to instruct the syslog daemon not to call sync after each write. With the traditional syslog daemon, make sure that all file names in /etc/syslog.conf have - before them, e.g.

auth,authpriv.*         -/var/log/auth.log

With rsyslog, also make sure that log file names have - before them; the log files are configured in /etc/rsyslog.conf and /etc/rsyslog.d/*.

CPU utilisation is easy:

From the command line:
while ( sleep 10 ) ; do cat /proc/loadavg >> mylogfile ; done

The sleep command will sleep 10 seconds and than return with the return value 0 (aka success). We abuse that to get a compact while( true ) sleep 10.

/proc/loadavg contains the load avarages of now, over the last 5 minutes, and over the last 15 minutes. If you are logging every 10 seconds then you are only interested in the first value.

Or in a script (using bash).

#!/bin/sh
# Using /bin/sh which is guaranteed to be present on any posix system.
# If you want to add shell specific parts in the script than replace this.
# E.g. if you want to use bash specific stuff then change it to:
# #!/usr/bin/env bash
# Make sure that the shebang is on the first line of the script (no comments above it!)

# While true, pause 10 seconds, then append information to Mylogfile
#
while ( sleep 10 ) ; do cat /proc/loadavg >> mylogfile ; done

We can add a cat /proc/meminfo to the information we append to the log file. /proc/meminfo is quite extensive and it will log a lot. If you only want to filter on specific memory information then please add that to the post.

The simplest form of that would result in:
while (sleep 10) ; do cat /proc/loadavg /proc/meminfo >> mylogfile ; done).