Explanation Given information: The weight of the machine ( W ) is 500 lb. The spring constant ( k ) is 250 lb/inch. The coefficient of damping ( c ) is 10 lb ⋅ s / in . . The periodic force is applied with a frequency ( f f ) is 2 cycles. The magnitude of the periodic force ( P m ) is 20 lb. The amplitude of the steady state vibration ( x m ) is 0.05 inch. The acceleration due to gravity ( g ) is 32 .2ft/s 2 . Calculation: The periodic force is applied with a frequency of 2.0 cycles per second or 2.0 Hz. Calculate the circular frequency of the periodic force ( ω f ) using the formula: ω f = f f 2 π Here, f f is the periodic force in Hz. Substitute 2.0 Hz for f f . ω f = 2 π ( 2.0 Hz ) = 12.5664 rad / s The system consists of two springs each with a spring constant of 250 lb / in . Thus, the spring constant of the system is given by two times the spring constant of 250 lb / in . . Calculate the spring constant of the system ( k ) for two springs using the relation: k = 2 k s p r i n g Here, k is the spring constant of the system and k s p r i n g is the spring constant of each spring. Substitute 250 lb / in . for k s p r i n g . k = 2 ( 250 lb / in . ) = 500 lb / in . = 500 lb 1 in . × 1 ft 12 in . = 6000 lb / ft Calculate the natural circular frequency ( ω n ) using the formula: ω n = k m Substitute 6000 lb / ft for k and 15.5280 lb ⋅ s 2 / ft for m . ω n = 6000 lb / ft 15.5280 lb ⋅ s 2 / ft = 19.657 rad / s Calculate the critical damping coefficient ( c c ) using the formula: c c = 2 m ω n Substitute 15.5280 lb ⋅ s 2 / ft for m , and 19.657 rad / s for ω n . c c = 2 ( 15.5280 lb ⋅ s 2 / ft ) ( 19.657 rad / s ) = 610.47 lb ⋅ s / ft The periodic force is applied with a frequency of 2

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Forced undamped vibrations

In mechanical engineering, vibration is expressed as the term that occurs due to an object's backward and forward movement about a point of equilibrium. Generally, there are three types of vibrations which are,

Videos

Question

Chapter 19.5, Problem 19.140P

To determine

The coefficient of damping (c).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.5, Problem 19.139P

Chapter 19.5, Problem 19.141P

Students have asked these similar questions

= The steel curved bar shown has rectangular cross-section with a radial height h = 6 mm and thickness b = 4mm. The radius of the centroidal axis is R = 80 mm. A force P = 10 N is applied as shown. Assume the steel modulus of 207,000 MPa and G = 79.3(103) MPa, repectively. elasticity and shear modulus E = Find the vertical deflection at point B. Use Castigliano's method for a curved flexural member and since R/h > 10, neglect the effect of shear and axial load, thereby assuming that deflection is due to merely the bending moment. Note the inner and outer radii of the curves bar are: r = 80 + ½ (6) = 83 mm, r₁ = 80 − ½ (6) = 77 mm 2 2 Sπ/2 sin² 0 d = √π/² cos² 0 d0 = Π 0 4 大 C R B P

The steel eyebolt shown in the figure is loaded with a force F = 75 lb. The eyebolt is formed from round wire of diameter d = 0.25 in to a radius R₁ = 0.50 in in the eye and at the shank. Estimate the stresses at the inner and outer surfaces at section A-A. Notice at the section A-A: r₁ = 0.5 in, ro = 0.75 in rc = 0.5 + 0.125 = 0.625 in Ri 200 F FA

I have the fallowing question and solution from a reeds naval arc book. Im just confused as to where this answer came from and the formulas used. Wondering if i could have this answer/ solution broken down and explained in detail. A ship of 7000 tonne displacement has a waterplane areaof 1500 m2. In passing from sea water into river water of1005 kg/m3 there is an increase in draught of 10 cm. Find the Idensity of the sea water. picture of the "answer" is attached

Chapter 19 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

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 coefficient of damping ( c ).

Solution Summary: The author explains the coefficient of damping, which is underset_21.4, the spring constant, and the circular frequency of the periodic force.

Concept explainers

Videos

The coefficient of damping (c).

Want to see the full answer?

Chapter 19 Solutions