A machine for treating a surface lying in an XY plane. The machine includes a body, a body plate, a cleaning plate, a drive assembly and an attachment assembly. The cleaning plate is located between the body plate and the XY plane. The drive assembly is connected to the cleaning plate to drive the cleaning plate with a cleaning vibration in an oscillating pattern parallel to the XY plane. The attachment assembly flexibly attaches the cleaning plate to the body plate to permit the cleaning plate to vibrate relative to the body plate and to isolate the cleaning vibration from the body. A connector is attached to the body for connecting to a member, such as a handle, to move the machine in the XY plane.