Piper Cub pilot reported violent shaking of the engine just after takeoff. After turning back to land and completing a safe landing it was discovered that a portion of the aluminum propeller blade tip had gone missing.

Narrative

After being cleared for takeoff on Runway XX; I climbed to about 800 ft. AGL and having passed the Runway end by 100 or 200 yards the Cub experienced sudden and very violent shaking. After taking maybe 5 seconds to collect my thoughts I communicated to the tower 'Piper Cub experiencing major engine problem.' I throttled to idle (it still shook violently); pushed over to a glide and began a left turn to land back on Runway XY. ATC immediately began redirecting the four or so other planes in the pattern to remained clear of ZZZ. As I completed turning to about 240 degrees the Tower asked if I was landing on downwind on XY and pointed out that there was a 5 or 7 knot tailwind component. I confirmed an intent to land on Runway XY and was cleared in. The rest of the landing was uneventful. Exiting the aircraft I found that 5 inches of aluminum propeller blade tip had gone missing. From first shake to wheels on the ground the episode lasted maybe a minute. My mistake was not giving the Tower any indication of my intentions on the initial call though I knew it would create traffic conflicts with aircraft on final for Runway XX.