The phrase "put your back into something" is often used to encourage someone to fully commit their effort and energy towards a task. However, there are several other ways to convey the same idea while using different words. One possible synonym would be to "give it your all," indicating a maximum level of effort. Another option could be to "throw yourself into" a task, which implies a wholehearted dedication. "Go the extra mile" is also a phrase that suggests going above and beyond what is expected. Finally, "buckle down" is a term that conveys a serious commitment to a task, with a focus on persistence and determination.