The natural frequency of vibration of a person is found to be \(5.2 \mathrm{~Hz}\) while standing on a horizontal floor. Assuming damping to be negligible, determine the following:

a. If the mass of the person is \(70 \mathrm{~kg}\), determine the equivalent stiffness of his body in the vertical direction.

b. If the floor is subjected to a vertical harmonic vibration of frequency of \(5.3 \mathrm{~Hz}\) and amplitude of \(0.1 \mathrm{~m}\) due to an unbalanced rotating machine operating on the floor, determine the vertical displacement of the person.

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k = 4000 N/m m - 100 kg/ 0-20% f(t) 500 cos 251 N FIGURE 3.38 Spring-mass system on inclined plane.