Explanation Write the expression for the ratio of the amplitudes after N cycles. x 0 x N = C e − ζ ω n t 0 C e − ζ ω n ( t 0 + N τ d ) x 0 x N = e ζ ω n N τ d (I) Here, the natural frequency is ω n , the damping ratio is ζ , the time period is τ d and the number of cycles is N . Write the expression for the logarithmic decrement ( δ N ) . δ N = ln ( x 0 x N ) δ N = ln ( e ζ ω n N τ d ) δ N = ζ ω n N τ d (II) Write the expression for the time period of the system ( τ d ) . τ d = 2 π ω n 1 − ζ 2 (III) Conclusion: Substitute, Equation (III) in Equation (II)

8th Edition

ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 8.2, Problem 31P

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The expression for viscous damping factor based on the measured amplitudes of x0 and xN.

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The expression for viscous damping factor based on the measured amplitudes of x 0 and x N .

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The expression for viscous damping factor based on the measured amplitudes of x0 and xN.

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