(a) Explanation Given information: The mass of the electromagnet ( m ) is 150 kg. The mass of the scrap steel ( M ) is 100 kg. The spring constant ( k ) is 60 kN/m. The coefficient of damping ( c ) is 300 N ⋅ s / m . Calculation: Calculate the natural circular frequency ( ω n ) using the formula: ω n = k m Substitute 60 kN/m for k and 150 kg for m . ω n = 60 × 1000 N/m 150 = 20 rad/s Calculate the critical damping coefficient ( c c ) using the formula: c c = 2 m ω n Substitute 150 kg for m and 20rad/s for ω n (b) To determine Find the maximum upward displacement ( x max ) .

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ISBN: 9781260663778

Author: BEER

Publisher: MCG

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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…

Question

Chapter 19.5, Problem 19.136P

(a)

To determine

Find the frequency of oscillation (ωd).

(b)

To determine

Find the maximum upward displacement (xmax).

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Chapter 19.5, Problem 19.135P

Chapter 19.5, Problem 19.137P

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Find the frequency of oscillation ( ω d ) .

Solution Summary: The author calculates the frequency of oscillation using the formula: (omega_d).

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Find the frequency of oscillation (ωd).

Find the maximum upward displacement (xmax).

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Chapter 19 Solutions