Skyhawk 172/Cutlass 172
Flight Crew Flight Instructor; Flight Crew Instrument
Distraction; Time Pressure; Troubleshooting
Aircraft Equipment Problem Less Severe
Flight Crew Landed As Precaution; Flight Crew Returned To Departure Airport
Aircraft
While doing a CFI spin flight; the student was in the middle of climbing out of a spin recovery when the engine popped and began to vibrate severely. Instructor had the student level off and reduce the throttle and then asked if the student felt the vibration; too. Student said yes and that the yoke was vibrating severely as well. Instructor and Student made the decision to return back to ZZZ.
C172 flight instructor reported a significant engine vibration and elected to return to the departure airport.