fig1 shows a connecting area of a handle 1 of an electric toothbrush for connecting to a brush attachment 13 of the invention shown in fig3 . the handle 1 is comprised of a plastic housing and all components required for operation such as an electric motor , a gear unit , batteries or storage batteries , a controller and the like . these components are in the interior of the housing and not shown . as illustrated in fig1 , a shaft 2 made in particular of metal projects directly out of the handle 1 and performs a small torsional oscillation about its longitudinal axis at a high frequency of 260 hz , approximately . in other words , the shaft 2 executes a vibratory motion when driven by an electric drive mechanism . other vibratory motions , such as those along the shaft axis 3 or a combination thereof for example , are also possible . this vibratory motion is directly transmitted to bristles 50 of the brush attachment 13 . the bristles 50 are fixedly secured to the brush attachment 13 either directly in a bristle area or by way of a replaceable bristle holder , not shown . however , the bristles 50 do not move relative to the brush attachment but only relative to the handle 1 . in other words , they move together with the brush attachment 13 . the vibratory motion of the bristles 50 is used for dental cleaning and dental care . the brush attachment 13 has a brush shank 12 — preferably made of plastic — in which a plug - on part 11 — preferably also made of plastic — is fastened by positive and / or frictional engagement therewith , being in particular snap - locked in the brush shank 12 by detent means . preferably , the brush shank 12 is shaped in an essentially tubular configuration and the plug - on part 11 is constructed as a sleeve . at one front face or end 21 of the brush attachment 13 or the plug - on part 11 is an approximately circular receiving opening in which the shaft 2 can be inserted . the brush attachment 13 is thus constructed to be pluggable onto and detachable from the shaft 2 of the handle 1 . the plug - on part 11 is equipped with a first spring element 35 acting directly on the shaft 2 , as shown in fig3 . this element is constructed as a detent element to engage with a detent notch 8 of the shaft 2 with a snap action . the first spring element has preferably a detent finger with an approximately v - shaped detent lug 36 , which engages in a v - shaped detent groove 8 of the shaft 2 such that the brush attachment 13 is also axially located relative to the shaft 2 , with the detent finger transmitting axial forces . the first spring element extends preferably axially in relation to the shaft 2 . with its free end the detent finger adjoins a cavity 37 of the plug - on part 11 , with material recesses 38 situated to the side of the detent finger . the brush attachment 13 is equipped in addition with a second spring element 30 arranged in an axially offset position relative to the first spring element 35 . according to the invention the second spring element 30 is arranged on the plug - on part 11 and acts likewise directly on the shaft 2 . as the result , the brush attachment 13 , or to be more precise the plug - on part 11 , takes support upon two axially spaced points of the shaft 2 , thus permitting the use of high drive frequencies . the axial distance a 5 ( cf . fig7 ) between the first spring element 35 and the second spring element 30 amounts to preferably 5 to 20 mm , particularly around 8 to 14 mm , e . g ., 12 mm , which is a good compromise between minimizing the sleeve dimensions and maximizing the noise damping . as fig4 and 5 show , the first spring element 35 and the second spring element 30 are arranged preferably in the same radial position , the second spring element 30 being arranged on an area close to the bristle carrier or the bristles 50 while the first spring element 35 is arranged at a location more remote from the bristle carrier , as illustrated in fig3 . the detent finger 35 points preferably in the direction of the handle 1 . as fig3 and 7 show , the second spring element 30 is comprised of an axially aligned spring bar with a bend curved toward the shaft 2 . this spring bar is constructed in particular as a bending bar . the spring bar lies between two axial slots 51 , 52 or recesses 31 ( fig4 ) of the plug - on part 11 . when the brush attachment 13 is plugged on , the spring bar 30 is bent slightly outwardly , its spring force operating to urge it directly against the shaft 2 , as shown in fig7 . the detent finger 35 presses likewise with its spring bar and / or detent lug 36 against the shaft 2 . the distance a 3 ( fig4 ) is smaller than the distance a 1 ( fig2 ). the difference is equal in particular to less than 1 mm . the spring action of the bent spring bar 30 is obtained necessarily by demolding when , after the plug - on part 11 is injection - molded , a core provided in the manufacturing process for this bent shape is withdrawn . the plug - on part 11 is equipped with a third spring element 22 in an axially offset position relative to the first two spring elements 30 , 36 , which lies preferably in the vicinity of the receiving opening or is arranged on the end 21 close to the handle 1 . the first spring element 35 then lies between the second spring element 30 and the third spring element 22 . as becomes apparent from fig6 , the third spring element 22 is comprised of several , in particular three , radially offset resilient fingers 53 - 55 , which in the mounted state also urge against the shaft 2 . the fingers 53 - 55 extend axially and point preferably toward the handle 1 and are relatively short , preferably only 1 to 3 mm long . free spaces 23 exist between the fingers 53 - 55 . in the non - inserted state the free ends of the fingers 53 to 55 adjoin a ( n only imaginary ) circular line 24 ( fig6 ) with a diameter d 3 . the diameter d 1 of the shaft 2 in this area is bigger than the diameter d 3 , thus producing a radial bias between a rear section 4 ( fig1 ) of the shaft 2 and the fingers 53 - 55 of the plug - on part 11 . as is shown in fig1 and 2 , the shaft 2 is constructed with several cross sectional areas , including one area with a circular cross section and a diameter d 1 in the vicinity of the handle 1 for the third spring element 22 , one area , which is roughly in the middle of the shaft 2 , with a likewise circular cross section and a somewhat smaller diameter d 2 for the first spring element 35 , and one forward area with a reduced cross section ( cf . a 1 in fig2 ) for the second spring element 30 on the free end of the shaft 2 . on this forward end close to the bristle carrier the shaft 2 has an essentially d - shaped cross section . in this region are two parallel surface areas 6 and 7 . the surface area 7 , which makes contact with the second spring element 30 , is smaller , for example ¼ to ¾ , in particular approximately half the size of the opposite surface area 6 . the surface area 6 lies in the vicinity of the axis 3 , while the flattening 7 or surface area 7 lies close to the circumference of a forward section 5 . the distance a 2 can be smaller than 1 mm , for example . the surface area 6 can also meet exactly with the axis 3 or even be arranged above it . the distance a 1 between the two surface areas equals preferably about 1 . 5 to 2 . 5 mm or approximately half the diameter d 2 . the diameter d 2 equals preferably 80 % to 97 % of the diameter d 1 and in particular 3 mm to 5 mm , for example 4 mm . the distance a 4 between the second and the third spring element 30 , 22 is relatively large and equals preferably 20 - 40 mm , particularly 23 - 27 mm . this is favorable for the transmission of bending moments between the shaft 2 and the plug - on part 11 . the third spring element 22 lies in the shaft area with the biggest diameter d 1 . the first spring element 35 lies in the area with the reduced diameter d 2 , and the second spring element 30 thus lies in the d - shaped forward area of the shaft . the plug - on part 11 encloses the d - shaped area such that the brush attachment 13 can be plugged onto the shaft 2 in a certain radial position only . a plane area 29 ( fig4 ) of the plug - on part 11 rests flush on the surface area 6 ( fig2 ) such that high torques can be transmitted . the spring bar 30 can transmit lateral forces and bending moments between the shaft 2 and the plug - on part 11 . a frontal insertion bevel 60 in the vicinity of the surface area 6 and a further insertion bevel 61 in the area of the diameter d 2 facilitate the plugging on such that the brush attachment 13 rotates into the correct position on its own . fig3 shows further that the plug - on part or the sleeve 11 is press - fitted into the brush shank or secured therein by frictional engagement , namely at points 14 and 15 at the ends respectively of the sleeve 11 . in axial direction the sleeve 11 is additionally fastened by positive engagement of an annular , outwardly extending fastening collar 16 with the brush shank 12 , for which a groove 17 is provided on the brush shank 12 . the sleeve 11 is thus held by in the brush shank 12 by both frictional and positive engagement therewith . fig8 and 9 illustrate a very advantageous embodiment of the brush attachment 13 with soft - elastic areas . the soft - elastic construction is useful in combination with the spring element arrangement of the invention . this construction , which is shown in fig8 or 9 , can also be used in combination with a different plug - on solution . the brush attachment 13 or the brush shank 12 has a soft - elastic padding 70 , 71 or 76 . this padding extends at least over a section of the brush attachment and covers preferably at least a rear side of the area set with bristles . in other words , this padding 70 or 71 is arranged preferably in a region proximate the bristles . a soft - elastic component , which forms the padding 70 or 71 , encompasses a hard part 72 or 73 , which lies in an area opposite the bristles 50 . the padding 71 extends preferably over a partial area , preferably about half of a circumference , and exists only in the vicinity of the bristles 50 . the soft - elastic component can cover in addition side areas of the brush attachment in full or in part , as shown in fig8 . as illustrated in fig1 , a soft - elastic padding 76 can also enclose the brush attachment 13 in full . the soft - elastic , in particular rubbery plastic mass is injection - molded using a two - component plastic injection - molding process . this elastic padding can have a structured , in particular studded or ribbed , surface , such that the brush shank is particularly good to grip . if the bristles 50 are omitted or replaced by massage elements , such a vibrating device with a soft - elastic component can also be used as a massaging device . a number of embodiments have been described . nevertheless , it will be understood that various modifications may be made without departing from the spirit and scope of the invention . accordingly , other embodiments are within the scope of the following claims . the foregoing embodiments are therefore to be considered in all respects illustrative rather than limiting of the invention described herein . the scope of the invention is thus indicated by the appended claims rather than by the foregoing description , and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced herein . 61 , 62 insertion bevels p 0 70 , 71 , 76 padding