A Piper Aztec pilot reported experiencing a significant vibration in the rudder pedals; accompanied by yaw oscillations; necessitating an immediate return to the departure airport. A post-flight inspection revealed a failed connecting rod to the rudder trim system.

Narrative

On Day 0; I planned flight from ZZZ to ZZZ1 to perform a camera system test. I departed from runway XX at XA:27. Shortly after takeoff; I experienced significant rudder pedal vibrations that propagated throughout the aircraft; resulting in rapid yaw oscillations. I immediately broadcast over the common traffic advisory frequency (CTAF) that I was returning to the airport.Attempts to climb exacerbated the buffeting and vibrations; particularly with changes in pitch or bank angle. I began troubleshooting by adjusting pitch and power settings and determined that maintaining airspeeds between 90-100 knots with reduced power and minimal control inputs significantly reduced the severity of the issue.I remained in a left-hand traffic pattern at approximately 500 to 600 feet AGL. During the approach and landing; as airspeed decreased; the vibrations and buffeting intensified. Despite this; I executed a safe landing on runway XY at XA:31.After shutdown; I conducted a post-flight inspection of the rudder and discovered that the rudder trim tab cable was completely disconnected from the connecting rod.The weather at the time of the incident: METAR: ZZZ Day 0 XA:30 AUTO 0000 10SM CLR 29/28 A2993 RMK AO2.