The following will copy the contents of the source_dir to the time-stamped folder.
$ cp -r ~/source_dir/ ~/backup_dir/$(date +%Y-%m-%d_%H:%M:%S)/
The following will copy the contents of the source_dir to the time-stamped folder.
$ cp -r ~/source_dir/ ~/backup_dir/$(date +%Y-%m-%d_%H:%M:%S)/