Need help diagnosing a throttle cable & gas pedal problem on my '67 Barracuda

The gas pedal on my 'Cuda is floppy and I can't figure out how to fix this. When I disconnect the linkage at the carb end and push/pull on the cable, the pedal moves up and down... so I don't think the cable is broken. The gas pedal pushes in but then the cable doesn't have tension to push the pedal back out. Who can help with suggestions or ideas? Thanks!