I would just hand animate it in your place since you desire such a simple motion and you don't want it to slow down over time either so there is no need for any complex simulation.
Select the top verticie of the cone in Edit mode than Shift+S to set cursor to selected,go back to Object mode and press W or Right click (depending on if you use right or left click select respectively) and Set Origin to 3D Cursor.
Than just rotate it 90 degrees on th X axis, press I to insert key frame and select Rotation. Go a few frames forward on the timeline depending on how long you want you swing to last than rotate 180 degrees in the other direction and instert another rotation keyframe.
From than swithc your timeline to dope sheet, B for box select and select your 2 frames. Shift+D to duplicate and slide them across the time line, tha rinse and repeat until you have enough frames for your animation.