From extensive biomechanical tests, the spinal stiffness k of a person is estima

Question

From extensive biomechanical tests, the spinal stiffness k of a person is estimated to be 50,000N/m. Assume that the body mass is 80 kg. Let us assume that this person is driving an automobile without wearing a seat belt. On hitting an obstacle, the driver is thrown upwards, and drops in free fall onto an unpadded seat and experiences an impulse with a magnitude of 100N?s. Determine the resulting motions if an undamped single degree-of-freedom model is used to model the vertical vibrations of this person.

Explanation / Answer

Frequency n = w / (2*pi)

= sqrt (k/m) / (2*3.14)

= sqrt (50000 / 80) / (2*3.14)

= 3.98 Hz

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