Engineering Mechanics: Dynamics, Student Value Edition (14th Edition)
14th Edition
ISBN: 9780134082424
Author: HIBBELER, Russell C.
Publisher: PEARSON
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Chapter 22.6, Problem 73P
To determine
The differential equation that describes the motion in terms of the angle of the bars rotation and the damping coefficient of the dashpot.
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Two blocks A and B, each of mass m , are supported as shown by three springs of the same constant k Block A and B are connected by a dashpot and block B is connected to the ground by two dashpots, each dashpot having the same coefficient of damping c Block A is subjected to a force of magnitude P=Pm sin wf t. Write the differential equations defining the displacements xA and xB of the two blocks from their equilibrium positions.
An 8-kgkg block is suspended from a spring having a stiffness k=80N/mk=80N/m.
If the block is given an upward velocity of 0.4 mm // ss when it is 90 mmmm above its equilibrium position, determine the equation which describes the motion of the block measured from the equilibrium position. Assume that positive displacement is measured downward.
Determine the maximum upward displacement of the block measured from the equilibrium position. Assume that positive displacement is measured downward.
Determine a natural frequency of vibration as a function of k₁, k₂. g and W of a spring-mass system placed on a inclined plane as shown in the figure:
Chapter 22 Solutions
Engineering Mechanics: Dynamics, Student Value Edition (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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- When a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it reaches rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 68(e^-2t)cos4t is applied to the system. Determine the equation of motion in the absence of damping.arrow_forwardThe block (mass not given) is subjected to the force F = (910 sin(5.3t)) N, where t is in seconds. The spring constant (of each of the springs) is k = 347 N/m. The damping ratio is c/cc = 0.69. If the natural frequency of vibrations is fn = 1.02 Hz, what is the amplitude (in meters) of the steady-state vibrations? Choose the correct answer: a) There is not enough information to solve b) 910.000 c) 1.107 d) 2.215 e) 0.049arrow_forwardThe piece has a mass of 43 kg and is supported by springs with a common spring constant of 4445 N / m. What is the frequency of the vibration of the body when a damper with a damping factor of 80 kg / s is added to the suspension? Enter the answer in Hertz to one decimal place.arrow_forward
- (machine dynamıc) Mass M is attached to the end of the rod of length L with mass m given in the figure on the right and it is connected to a fixed support with a spring with a coefficient of k.a- Obtain the expression that gives the natural frequency of the system for the situation in the figure.b- Explain how the natural frequency of the system is affected if the spring coefficient increases and/or decreases as 0.5k, 2k, 5k.arrow_forwardA mass weighing 5 pounds is attached to a spring whose constant is k = 7lb/tf. The medium offers a damping force that is foot numerically equal to the instantaneous velocity. The mass is released from a point 1 ft above the equilibrium position with a downward velocity of 8 ft/seg. Determine the equation of motion x(t) of this systemarrow_forwardThe device has a mass of 180 kg and a specific frequency of 100 Hz. What is the vibration amplitude transfer to the substrate when Vibration Insulators with a spring constant of 9.6 MN / m are installed under the device? There are 4 springs under the device, and the spring constants of the parallel springs add up. Enter the answer to two decimal places.arrow_forward
- given that the specific weight of the spring material is 56.6 kN/m3, find the lowest critical frequency of the spring. Express your answer in rpm,arrow_forwardA bullet of mass m= 103.4 Grams has a velocity of v0= 62 m/s just before it strikes the target of mass M=4 Kilograms, If the bullet embeds in the target, and the vibration is to be critically damped, determine the dashpot’s critical damping coefficient. The stiffness of each spring is k= 1,326 N/marrow_forwardIt is desired to adjust the damping of the passenger car's suspension so that the vibration is damped to one tenth of the original during one oscillation. Based on this, determine the relative attenuation constant D (give the answer to two decimal places). The car has a mass of 1500 kg and the body frequency is 1.32 Hz.arrow_forward
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