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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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
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.
The 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 slip
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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- 4. 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_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_forwardSuppose 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_forward
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