(a) Explanation Given information: The unbalance weight ( w ) is 14 oz. The radius of the circle ( r ) is 6 inch. The weight of the system ( W ) is 300 lb. The speed of the exciter ( N ) is 1200 rpm. The amplitude of vibration ( x m ) is 0.6 inch. The acceleration due to gravity ( g ) is 32.2 ft / s 2 . Calculation: Convert the unit of unbalance weight ( w ) from oz to lb: w = ( w ) oz × 1 lb 16 oz Here, ( w ) oz is the unbalance weight. Substitute 14 oz for ( w ) oz . w = 14 oz × 1 lb 16 oz = 0 .875 lb Calculate the mass of the unbalance weight ( m ) using the formula: m = w g Substitute 0.875 lb for w and 32.2 ft / s 2 for g . m = 0.875 lb 32.2 ft / s 2 = 0.02717 lb ⋅ s 2 / ft Calculate the mass of the system ( M ) using the formula: M = W g Substitute 300 lb for W and 32.2 ft / s 2 for g . M = 300 lb 32.2 ft / s 2 = 9.3167 lb ⋅ s 2 / ft Calculate the frequency of the periodic force ( ω f ) using the relation: ω f = 2 π N 60 Substitute 1200 rpm for N . ω f = 2 π ( 1 , 200 rpm ) 60 = 125 (b) To determine The damping factor ( c c c ) .

12th Edition

ISBN: 9781260265453

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

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 19.143P

(a)

To determine

The combined spring constant (k).

(b)

To determine

The damping factor (ccc).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.5, Problem 19.142P

Chapter 19.5, Problem 19.144P

Students have asked these similar questions

A three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a known weight at a known distance from the axis of rotation and to measure the frequency of oscillations after releasing it from rest with a small initial angle. In this case, a weight of Wadd = 50 lb is attached to one of the blades at a distance R = 20 ft from the axis of rotation. Knowing that when the blade with the added weight is displaced slightly from the vertical axis, and the system is found to have a period of 7.6 s, determine the centroidal mass moment of inertia of the three-blade rotor.

As shown in the Fig. 3, the CM of a cylinder of mass m and radius R is connected to the top of hoop of mass m by a spring. The spring constant is assumed to be known and it is denoted by k. At a given moment the system is slightly compressed and then suddenly released. After the release, both rigid objects roll without slipping. Determine the angular frequency of the resulting oscillation. It is assumed that the spring remains horizontal throughout the motion. Figure 3: Coupled Oscillator

2. A point mass m is strung on a vertical ring of radius R, and it oscillates freely with respect to its equilibrium point located at the lowest point of the ring. An external moment of force is applied that causes the ring to oscillate about its center in the form α = α₁ cost where a is the angle of rotation. Determine the general movement of the mass m, and under what circumstances this movement enters into resonance, detailing this phenomenon.

Chapter 19 Solutions

VECTOR MECH...,STAT.+DYN.(LL)-W/ACCESS

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - Prob. 19.7P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9P Ch. 19.1 - Prob. 19.10P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The combined spring constant ( k ).

Solution Summary: The author calculates the mass of the unbalance weight using the formula: m=wg.

Concept explainers

The combined spring constant (k).

The damping factor (ccc).

Want to see the full answer?

Chapter 19 Solutions