Explanation Write the expression for the natural frequency of the system ( ω n ) . ω n = 2 k m (I) Here, the spring constant is k and the mass of the unit is m . Write the expression for the damping ratio ( ζ ) . ζ = 2 c 2 m ω n (II) Here, the coefficient of damping is c . Write the expression for the magnification factor ( M ) . M = 1 [ 1 − ( ω ω n ) 2 ] 2 + [ 2 ζ ( ω ω n ) ] 2 (III) Write the expression to find the speed of the motor ( N ) . N = 60 ω 2 π (IV) Conclusion: Substitute, 2.1 kN / m for k and 20 kg for m in Equation (I). ω n = 2 ( 2.1 kN / m × 1000 N 1 kN ) 20 kg ω n = 14.49 rad / s Substitute, 58 N ⋅ s / m for c , 14.49 rad / s for ω n and 20 kg for m in Equation (II)

8th Edition

ISBN: 9781118885840

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

Publisher: WILEY

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

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Chapter 8.3, Problem 57P

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The speed range of the motor.

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