Please help solve this problem, full working is appreciated... A shaft is suppor

Question

Please help solve this problem, full working is appreciated...

A shaft is supported by bearings at A and B as shown in the following diagram. The axial locations for planes containing out-of-balance masses C and D are also depicted. Out-of-balance at C is equivalent to 0.6 kg mass at a radius of 40 mm. Out-of-balance at D is equivalent to 0.8 kg mass at a radius of 60 mm. Determine the magnitude and the angular location (with respect to C) of the bearing reaction forces when the shaft rotates at 125 rpm.

Explanation / Answer

the kinetic energy of the shaft at point C is

K1 = (1/2)m1 x r1^2 x w^2

similarly,at point D

K2 = (1/2)m2 x r2^2 x w^2

we know that

K = F x S

or F = (K/S)

where F is force and S is displacement

therefore the reaction forces F1 and F2 are calculated

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