Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.6, Problem 69P
To determine
Show that if the damping coefficient
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Q/ A uniformrigid bar of maSs m is pivoted
at one end and connected symmetrically by twe
springs and dampers at thi other end. The bar
is strtchid initially by an angle@ and released.
from rest. If m=10 kg, K=2000 N/w
Ce13 N.Sec/m and L-5m. find the damping
ratio g and the uatural frequency.
Which of the following statements are valid for the rod below that is undergoing fixed axis rotation about pin O, where the spring constant is k = 115 N/m and the damping coefficient is c = 302 N.s/m? The slender rod has mass m = 17 kg and length L = 0.6 m. The differential equation governing the motion of the rod is given below. (In the statements below, wn denotes the natural frequency ωn, while wd denotes the damped frequency ωd.)
a) Damped vibration, wn and wd not applicable
b) Underdamped, wn = 2.60 rad/s, wd = 17.57 rad/s
c) Overdamped, wn = 2.25 rad/s, wd not applicable
d) Overdamped, wn = 2.60 rad/s, wd not applicable
e) Underdamped, wn = 2.25 rad/s, wd = 26.55 rad/s
Chapter 22 Solutions
Engineering Mechanics: Dynamics (14th Edition)
Ch. 22.1 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22.1 - Prob. 2PCh. 22.1 - A spring is stretched 200 mm by a 15-kg block. If...Ch. 22.1 - When a 20-lb weight is suspended from a spring,...Ch. 22.1 - Prob. 5PCh. 22.1 - Prob. 6PCh. 22.1 - Prob. 7PCh. 22.1 - Prob. 8PCh. 22.1 - A 3-kg block is suspended from a spring having a...Ch. 22.1 - Prob. 10P
Ch. 22.1 - Prob. 11PCh. 22.1 - 22-12. Determine the natural period of vibration...Ch. 22.1 - The body of arbitrary shape has a mass m, mass...Ch. 22.1 - Determine the torsional stiffness k, measured in...Ch. 22.1 - Prob. 15PCh. 22.1 - Prob. 16PCh. 22.1 - If the natural periods of oscillation of the...Ch. 22.1 - Prob. 18PCh. 22.1 - Prob. 19PCh. 22.1 - A uniform board is supported on two wheels which...Ch. 22.1 - If the wire AB is subjected to a tension of 20 lb,...Ch. 22.1 - The bar has a length l and mass m. It is supported...Ch. 22.1 - The 20-kg disk, is pinned at its mass center O and...Ch. 22.1 - Prob. 24PCh. 22.1 - If the disk in Prob. 22-24 has a mass of 10 kg,...Ch. 22.1 - Prob. 26PCh. 22.1 - Prob. 27PCh. 22.1 - Prob. 28PCh. 22.1 - Prob. 29PCh. 22.2 - Determine the differential equation of motion of...Ch. 22.2 - Determine the natural period of vibration of the...Ch. 22.2 - Determine the natural period of vibration of the...Ch. 22.2 - Prob. 33PCh. 22.2 - Determine the differential equation of motion of...Ch. 22.2 - Prob. 35PCh. 22.2 - Prob. 36PCh. 22.2 - Prob. 37PCh. 22.2 - Prob. 38PCh. 22.2 - Prob. 39PCh. 22.2 - If the slender rod has a weight of 5 lb, determine...Ch. 22.6 - If the block-and-spring model is subjected to the...Ch. 22.6 - Prob. 42PCh. 22.6 - A 4-lb weight is attached to a spring having a...Ch. 22.6 - Prob. 44PCh. 22.6 - Prob. 45PCh. 22.6 - Prob. 46PCh. 22.6 - Prob. 47PCh. 22.6 - Prob. 48PCh. 22.6 - Prob. 49PCh. 22.6 - Prob. 50PCh. 22.6 - The 40-kg block is attached to a spring having a...Ch. 22.6 - The 5kg circular disk is mounted off center on a...Ch. 22.6 - Prob. 53PCh. 22.6 - Prob. 54PCh. 22.6 - Prob. 55PCh. 22.6 - Prob. 56PCh. 22.6 - Prob. 57PCh. 22.6 - Prob. 58PCh. 22.6 - Prob. 59PCh. 22.6 - The 450-kg trailer is pulled with a constant speed...Ch. 22.6 - Prob. 61PCh. 22.6 - Prob. 62PCh. 22.6 - Prob. 63PCh. 22.6 - The spring system is connected to a crosshead that...Ch. 22.6 - Prob. 65PCh. 22.6 - Prob. 66PCh. 22.6 - Prob. 67PCh. 22.6 - The 200-lb electric motor is fastened to the...Ch. 22.6 - Prob. 69PCh. 22.6 - If two of these maximum displacements can be...Ch. 22.6 - Prob. 71PCh. 22.6 - Prob. 72PCh. 22.6 - Prob. 73PCh. 22.6 - Prob. 74PCh. 22.6 - Prob. 75PCh. 22.6 - Prob. 76PCh. 22.6 - Prob. 77PCh. 22.6 - Prob. 78PCh. 22.6 - Prob. 79P
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- An sdof system consists of mass 175 kg and a spring constant k 530 kn/m while testing the system a relative velocity of 0.3 m was observed on application of force of 450 n determine the damping ratioarrow_forwardThe disk rolls without slip a. What is the critical damping coefficient, c for the system? b. Plot the response of the system when the center of the disk is displaced 5 mm from equilibrium and released from rest, if: i. c= cd/2 r= 40 cm 4 kN/m thin disk of mass m = 1 kg. no sliparrow_forwardSolve a,b,c and for c when the two dampers are connected to rigid bar (not parallel or series)arrow_forward
- Needs Complete solution with 100 % accuracy.arrow_forwardShow the complete solution of the given problem. The answers are answers are: Cc = 24.787 Wn = 51.64 Wd = 44.72 Keq = 640 Ieq = 0.24 df = 1/2 Xo = 5mm Vo = 0arrow_forward4. Problem 2: Consider the block diagram shown in the figure below. Determine the values of K and k such that the system has a damping ratio & = 0.7 and an undamped natural frequency wn = 4 rad/s. Please, use the block diagram algebra and the secondarrow_forward
- Suppose that the motion of the adjustable roller has a damping coefficient b, and that the force exerted by the rolled material on the adjustable roller is proportional to the material's change in thickness: f=c(T-x). Suppose further that the DC motor has a torque constant K, and a back- emf constant Ke, and that the rack-and-pinion has effective radius of r. In reality the thickness of the input material. T. is one of the inputs. but here for simplicitv assume T is constant. Do not neglect the weight of the adjustable roller and assume mg = cT. The input of the system is the voltage of DC-motor and the output is the thickness of the output material ,x. 1. Draw free body diagram of adjustable roller 2. Prepare a mathematical block diagram showing mathematical relations in terms of the transfer functions. The block diagram should at least contains a block for DC-motor and a block for mechanical system (i.e gears and adjustable rollers) 3. Determine transfer function G(s)=X(s)/Vs(s) 4.…arrow_forward5. An electric motor with 34 kg of mass, rated speed of 3932 rpm and unbalance of 0.002 kg.m must be mounted on an insulator for a force transmissibility of 0.167. Determine the stiffness of the insulator. Consider zero damping.arrow_forwardA mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c ). The mass is set in motion with initial position xo and initial velocity vo. Find the position function x(t) and determine whether the motion is overdamped, critically damped, or underdamped. If it is underdamped, write the position function in the form x(t) =C, e -p' cos (@,t-a,). Also, find the undamped position function u(t) = Co cos (@ot – ao) that would result if the mass on the spring were set in motion with the same initial position and velocity, but with the dashpot disconnected (so c=0). Finally, construct a figure that illustrates the effect of damping by comparing the graphs of x(t) and u(t). c= 4, k = 6, xo =3, vo = 0 m =arrow_forward
- tion 2: a. Determine the differential equation of motion and find the natural frequency (w). Also establish the critical damping for the system shown in Fig. 2a Earrow_forwardfor the system shown in Fig. (2) the values m = 1,750 kg, c = 3,500 N-s/m, k = 7x 105N/m, a = 1.25 m and b = 2.5 m. 1. Draw F.B.D. 2. find equation of motion & wd. 3. 4. Determine the value of the critical damping. Calculate time response. k rigid link marrow_forwardPlease answer immediatelyarrow_forward
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