a) Explanation Write the expression for the natural frequency of the system ( ω n ) . ω n = k m (I) Here, the spring constant is k and the mass is m . Write the expression for the damping ratio ( ζ ) . ζ = c 2 m ω n (II) Here, the damping coefficient is c . Write the expression for amplitude of the mass ( X ) . X = F 0 / k { [ 1 − ( ω ω n ) 2 ] 2 + [ 2 ζ ( ω ω n ) ] 2 } 1 2 (III) Here, the static load is F 0 , the frequency ratio is ( ω ω n ) and the damping ratio is ζ . Conclusion: Substitute, 100 kN / m for k and 10 kg for m in Equation (I) . ω n = 100 kN / m ( 1000 N 1 kN ) 10 kg ω n = 100 rad / s Substitute, 500 N ⋅ s / m for c , 10 kg for m and 100 rad / s for ω n in Equation (II) b) To determine The amplitude of steady state motion of the mass when c = 0 .

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 46P

To determine

The amplitude of steady state motion of the mass when c=500N⋅s/m.

To determine

The amplitude of steady state motion of the mass when c=0.

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Chapter 8.3, Problem 45P

Chapter 8.3, Problem 47P

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The amplitude of steady state motion of the mass when c = 500 N ⋅ s / m .

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The amplitude of steady state motion of the mass when c=500N⋅s/m.

The amplitude of steady state motion of the mass when c=0.

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Chapter 8 Solutions