awkを使えばvmstatだけではなくなんにでも日時をつけることが出来ます。
vmstatに日時をつける
vmstat 1|awk '{print strftime("%Y/%m/%d %H:%M:%S",systime()) " " $0 }'
2019/06/13 09:27:35 procs -----------memory---------- ---swap-- -----io---- --system-- -----cpu-----
2019/06/13 09:27:35 r b swpd free buff cache si so bi bo in cs us sy id wa st
2019/06/13 09:27:35 2 0 0 265972 12900 233000 0 0 274 163 511 423 15 2 83 0 0
2019/06/13 09:27:36 0 0 0 296276 12900 233116 0 0 0 5072 593 2685 31 3 66 0 0
2019/06/13 09:27:37 0 0 0 296160 12900 233296 0 0 0 0 397 300 14 0 86 0 0
2019/06/13 09:27:38 0 0 0 296160 12908 233484 0 0 0 28 428 329 14 0 85 0 1
2019/06/13 09:27:39 0 0 0 296036 12908 233704 0 0 0 0 488 393 14 1 85 0 0
2019/06/13 09:27:40 0 0 0 295788 12908 233932 0 0 0 0 465 343 14 0 86 0 0
2019/06/13 09:27:41 1 0 0 295540 12908 234148 0 0 0 0 424 311 13 2 85 0 0
2019/06/13 09:27:42 0 0 0 295292 12908 234348 0 0 0 0 431 310 14 1 85 0 0
2019/06/13 09:27:43 0 0 0 295168 12916 234492 0 0 0 12 431 325 13 1 86 0 0
tail -f したデータに日時をつける
tail -f access_log | awk '{print strftime("%Y/%m/%d %H:%M:%S",systime()) " " $0 }'
2019/06/13 09:31:14 1.2.3.4 - - [13/Jun/2019:09:09:08 +0000] "GET / HTTP/1.1" 200 479 "-" "Mozilla/5.0 (Macintosh; Intel Mac OS X 10.13; rv:56.0) Gecko/20100101 Firefox/56.0 Waterfox/56.2.10"
2019/06/13 09:31:14 1.2.3.4 - - [13/Jun/2019:09:09:08 +0000] "GET /css/demo.css HTTP/1.1" 304 - " "Mozilla/5.0 (Macintosh; Intel Mac OS X 10.13; rv:56.0) Gecko/20100101 Firefox/56.0 Waterfox/56.2.10"
2019/06/13 09:31:14 1.2.3.4 - - [13/Jun/2019:09:09:08 +0000] "GET /js/jquery.min.js HTTP/1.1" 304 - "" "Mozilla/5.0 (Macintosh; Intel Mac OS X 10.13; rv:56.0) Gecko/20100101 Firefox/56.0 Waterfox/56.2.10"