A 7-month-old baby was brought Wednesday to Northwest Medical Center, where doctors found the boy to have suspicious injuries.
Under questioning, the baby's father, Travis Fox, 24, of Springdale, told investigators "that he violently shook the child for an extended amount of time because the child was 'fussing,'''police said in a news release.
"He demonstrated the shake and it was violent," the release said.
Authorities said Fox acknowledged that he drank five beers before shaking the baby.
While the baby's death was being investigated, Springdale officers learned that Fox was under investigation for the Sept. 4, 2011, death of another of his children, a 6-month-old boy.
A Washington County sheriff's detective interviewed Fox about the baby's death in 2011.
"Mr. Fox admitted that he shook his 6-month-old son for 30-45 seconds because he was 'fussing,'" according to a prosecutor's report. "Mr. Fox said he was angered and tired because he was up for two days without sleep."
The report says Fox told the investigator that he admitted drinking tequila the day of the first death and that he'd tossed the child on a chair.
"Mr. Fox admitted he needs help for his anger," the report said.
It was unclear Thursday whether Fox had an attorney. He was being held without bond at the Washington County Jail.