An apparatus comprising: a static engine structure; at least one shaft (40; 50; 106) that rotates relative to the static engine structure; and a bearing assembly that supports the shaft (40; 50; 106), wherein the bearing assembly includes at least one first bearing hard mounted directly between the shaft (40; 50; 106) and the static engine structure, at least one second bearing mounted between the shaft (40; 50; 106) and the static engine structure, wherein the at least one second bearing includes a damper, and at least one third bearing mounted between the shaft (40; 50; 106) and the static engine structure, wherein the at least one third bearing includes a resilient member in parallel combination with a viscous damper, wherein the bearing assembly further includes at least one fourth bearing that is hard mounted directly between the shaft (40; 50; 106) and the static engine structure, and wherein the at least one second bearing is downstream of the at least one first bearing, the at least one third bearing is downstream of the at least one second bearing, and the at least one fourth bearing is downstream of the at least one third bearing; and characterised by the at least one fourth bearing including an inner race that has a first centerline and an eccentric outer race that has a second centerline that is radially offset from the first centerline. a static engine structure; at least one shaft (40; 50; 106) that rotates relative to the static engine structure; and a bearing assembly that supports the shaft (40; 50; 106), wherein the bearing assembly includes at least one first bearing hard mounted directly between the shaft (40; 50; 106) and the static engine structure, at least one second bearing mounted between the shaft (40; 50; 106) and the static engine structure, wherein the at least one second bearing includes a damper, and at least one third bearing mounted between the shaft (40; 50; 106) and the static engine structure, wherein the at least one third bearing includes a resilient member in parallel combination with a viscous damper, wherein the bearing assembly further includes at least one fourth bearing that is hard mounted directly between the shaft (40; 50; 106) and the static engine structure, and wherein the at least one second bearing is downstream of the at least one first bearing, the at least one third bearing is downstream of the at least one second bearing, and the at least one fourth bearing is downstream of the at least one third bearing; and characterised by the at least one fourth bearing including an inner race that has a first centerline and an eccentric outer race that has a second centerline that is radially offset from the first centerline. at least one first bearing hard mounted directly between the shaft (40; 50; 106) and the static engine structure, at least one second bearing mounted between the shaft (40; 50; 106) and the static engine structure, wherein the at least one second bearing includes a damper, and at least one third bearing mounted between the shaft (40; 50; 106) and the static engine structure, wherein the at least one third bearing includes a resilient member in parallel combination with a viscous damper, wherein the bearing assembly further includes at least one fourth bearing that is hard mounted directly between the shaft (40; 50; 106) and the static engine structure, and wherein the at least one second bearing is downstream of the at least one first bearing, the at least one third bearing is downstream of the at least one second bearing, and the at least one fourth bearing is downstream of the at least one third bearing; and characterised by the at least one fourth bearing including an inner race that has a first centerline and an eccentric outer race that has a second centerline that is radially offset from the first centerline.