Rod AB is rigidly attached to the frame of a motor running at a constant speed. When
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Rod AB is rigidly attached to the frame of a motor running at a constant speed. When a collar of mass m is placed on the spring, it is observed to vibrate with an amplitude of 15 mm. When two collars, each of mass m, are placed on the spring, the amplitude is observed to be 18 mm. What amplitude of vibration should be expected when three collars, each of mass m, are placed on the spring? (Obtain two answers.)
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a One collar b Two collars c Three collars xm 15 mm xm 18 mm 0 1 and x 0 However correspondingly either 0 or 0 0 k 02 m k 2 m 2 co k 1 5 unknown m 22 3m We also note that the amplitude of the displacement of the base remains constant Referring to Sec 197 Fig 199 we note that since xx and 2 n may be either 1 or 1 with x being we must have 1 Assuming x 0 xm For two collars 8m xm 0 For one collar 15 mm 18 mm Sm 12 00 2 1 2 Dividing 2 by 1 member by member 12 For three collars Substituting into 1 2 Assuming x 0 1 12 For two collars we have 12 1 12 we find Dividing 3 by 1 member by member F Sm 15 mm xm 3 13 00 8m 18 mm 1224 1 90 12 mm 13 m mm n 90 mm x3 225 mm 3 00 22 34 For three collars 11 17 Substitute into 1 8 15 mm 13 2 17 17 xm 8m 13 mm 17 11 17 0 0 n out of phase 3 9 mm 16 xm 3 563 mm Points corresponding ...View the full answer
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