How to make a timespan column based on a time stamp column?

I have a datatable with timestamps in column 1 and events in column 2. The timestamps have the format Y-m-d H:M:OS3 (e.g. "2019-09-26 07:29:22,778").

I would like to add a new column with time-span values of the difference between timestamp 2 to timestamp 1, then 3 to 1 etc. E.g.:

timestamp                  event           diff in sec
2019-09-26 07:29:22,778    X                   
2019-09-26 07:29:23,918    Y               1.140
2019-09-26 07:29:25,118    Z               2.340
.
.

Solution

In base:

dt1$timediff <- cumsum(c(0, difftime(tail(dt1$timestamp,-1), head(dt1$timestamp,-1))))

or using data.table:

library(data.table)

dt1[ , timediff := cumsum(c(0, diff(as.numeric(timestamp))))][]
#>                  timestamp event timediff
#> 1: 2019-09-26 07:29:22.778     X     0.00
#> 2: 2019-09-26 07:29:23.917     Y     1.14
#> 3: 2019-09-26 07:29:25.118     Z     2.34

Another dplyr solution base off of akrun's answer:

library(dplyr)
dt1 %>%
  mutate(difftime = difftime(timestamp, timestamp[1], unit = 'sec'))

Data: N.B: I am using data.table to read the data.

fread(text="date time  event
 2019-09-26 07:29:22.778    X                   
 2019-09-26 07:29:23.918    Y               
 2019-09-26 07:29:25.118    Z") -> dt1

dt1$timestamp <- as.POSIXct(paste(dt1$date, dt1$time), format="%Y-%m-%d %H:%M:%OS")

dt1 <- dt1[,4:3]