Question

Consider a single degree of freedom system comprising a mass M, supported on a spring and a dashpot as shown in the figure.

If the amplitude of the free vibration response reduces from 8 mm to 1.5 mm in 3 cycles, the damping ratio of the system is______ (round off to three decimal places).

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Answer :

Correct answer is : 0.088

x 0 x 3 = 8 1.5 = 80 15

x 0 x 1 x 1 x 2 x 2 x 3 = 80 15

e δ e δ e δ = 80 15 e 3 δ = 80 15

3 δ = ln ( 80 15 ) δ = 0.55799

2 π ξ 1 ξ 2 = 0.5579 ξ = 0.088

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