Question Solved1 Answer A reciprocating machine weighing 100kN is known to develop vertically oriented harmonic forces having and amplitude of 2.5kN at its operating speed of 40HZ. In order to limit the vibrations excited in the building in which the machine is installed, it is to be supported by a spring at each corner of its rectangular base. The designer wants to know what support spring stiffness would be required to limit to 0.4kN, the total harmonic force transmitted from the machine to the building.

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Transcribed Image Text: A reciprocating machine weighing 100kN is known to develop vertically oriented harmonic forces having and amplitude of 2.5kN at its operating speed of 40HZ. In order to limit the vibrations excited in the building in which the machine is installed, it is to be supported by a spring at each corner of its rectangular base. The designer wants to know what support spring stiffness would be required to limit to 0.4kN, the total harmonic force transmitted from the machine to the building.
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Transcribed Image Text: A reciprocating machine weighing 100kN is known to develop vertically oriented harmonic forces having and amplitude of 2.5kN at its operating speed of 40HZ. In order to limit the vibrations excited in the building in which the machine is installed, it is to be supported by a spring at each corner of its rectangular base. The designer wants to know what support spring stiffness would be required to limit to 0.4kN, the total harmonic force transmitted from the machine to the building.
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Step 1Given:F=2.5 KNf=40 Hznumber of springs,n=4FT=0.4 KNStep 2Transmissibility ratio is given by:FTF=1+(2ξr)2(1-r2)2+(2ξr)2where,ξ is damping ratio which in this case is 1.r=ffn      fn is natural frequency0.42.5=1+(2r)2(1-r2)2+(2r)20.42.5=1+4r21+r4-2r2+4r2(0.42.5)2=1+4r21+r4+2r20.0256=1+4r21+r4+2r20.0256+0.0256r4+0.0512r2=1+4r20.0256r4-3.9488r2-0.9744=0r= ... See the full answer