Five-week-old Sean Clark had suffered 71 rib fractures when he was found dead in his cot at his father’s home near Bristol in January 2018.
James Clark, 31, of Neads Drive, Warmley, had denied being responsible for Sean’s death but was found guilty of murder by a jury in August.
He was jailed for life with a minimum of 15 years at Bristol Crown Court.
Sean’s mother, Helen Jeremy, 27, of Russell Avenue, Kingswood, was cleared of causing or allowing the death of a child.
The court previously heard Sean was assaulted on at least three occasions during his short life, suffering 71 rib fractures and traumatic head injuries.
Ms Jeremy lived with Sean at her parents’ home in Kingswood and Clark lived with his mother in Warmley, and at weekends they would stay at each other’s homes with Sean.
Hours after arriving at Clark’s home on 11 January, Ms Jeremy used her phone to search on Google about babies coughing up blood.
She also sent her mother text messages indicating concerns for Sean’s welfare, saying he was crying a lot, particularly when he was picked up and during feeding.
On Sunday morning, Ms Jeremy woke up to find Sean unresponsive in his cot and the emergency services were called.
‘Harrowing evidence’
Sentencing Clark, judge Mr Justice Butcher said his crimes had “had a profound effect on members of Sean’s family and particularly on his mother”.
He said Sean had died of a brain injury “caused by being shaken, exacerbated by injuries to his rib cage caused by squeezing”.
“What exactly happened we don’t know because you have not said,” he said.
“But the jury has found you inflicted those injuries. The sentence for murder is fixed by law. Imprisonment for life.”
A spokeswoman for the Crown Prosecution Service, said Sean was the victim of a “number of serious assaults in the weeks before he died”.
“These attacks resulted in a series of horrific injuries and eventually in Sean’s tragic death,” she said,
“Cases involving the death of a child are distressing for everyone involved. This includes the jury, who were presented with harrowing evidence from some of top medical experts in the country, and who found James Clark guilty of murder.”