A free vibration of the mechanical system shown in Figure 8-27(a) indicates that the amplitude of vibration decreases to $25%$ of the value at $t = t_{0}$ after four consecutive cycles of motion, as Figure 8-27(b) shows. Determine the viscous-friction coefficient $b$ of the system if $m = 1 kg$ and $k = 500 N / m$ . (a) (b) Figure 8-27 (a) Mechanical system: (b) portion of a free-vibration curve.

Question

A free vibration of the mechanical system shown in Figure 8-27(a) indicates that the amplitude of vibration decreases to

25%

of the value at

t = t_{0}

after four consecutive cycles of motion, as Figure 8-27(b) shows. Determine the viscous-friction coefficient

b

of the system if

m = 1 kg

and

k = 500 N / m

. (a) (b) Figure 8-27 (a) Mechanical system: (b) portion of a free-vibration curve.

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