Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.6, Problem 76P
To determine
The differential equation of motion for the damped vibratory system and the type of motion.
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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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- The measurements on a mechanical vibrating system show that it has a mass of 8 kg and that the springs can be combined to give an equivalent spring of stiffness 5.4 N/mm. If the vibrating system have a dashpot attached which exerts a force of 40 N when the mass has a velocity of 1 m/s, find : 1. critical damping coefficient, 2. damping factor, 3. logarithmic decrement, and 4. ratio of two consecutive amplitudes.arrow_forwardConsider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?arrow_forwardfor the system shown determine the natural frequency and the damping factorarrow_forward
- Determine the natural frequency of the system shown beside using Equilibrium Methodarrow_forwardAn electric motor of mass 25 kg is supported on a three-spring system. Thesprings are arranged in parallel, with the three stiffnesses being 10 kN/m,5 kN/m and 25 kN/m respectively. Viscous damping is present within the systemand has a magnitude of 0.4 kNs/m.i) Produce a sketch of the system and state its equation of motion.ii) Determine the damping ratio and comment on its value.iii) Determine the amplitude of vibration of the motor 5 cycles afterit is released from an initial displacement of 15 mm.arrow_forwardA 1-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal frictionless surface. This block oscillates with an amplitude of 0.3 m and reaches a maximum speed of 5 m/s. What is the spring constant in N/m?arrow_forward
- 1. Explain_why_the_natural_frequency_measurements_should_better_reflect_the_system’s_true_undamped natural_frequency_(and_therefore_correlate_better_with_calculated_values)_than_the_frequency_of_oscillation measurements. 2. For_a Linear Spring-Mass System, Torsional Spring-Mass System, and Simple Pendulum System: identify_the_necessary_measurements_required_to_identify_the_natural_frequency_and the damping_ratio_for_the_linear_SMD_and_the_simple_pendulum.arrow_forwardDerive the expression for motion and determine the natural frequency of the system shown in the figure below. Neglect the mass of the rod.arrow_forwardBy what factor does the amplitude change in one period of these damped oscillations?arrow_forward
- A uniform rigid mass of 2 lb is hinged at its centre and laterally supported at one end by a spring of constant k=300 N/m. If the equation obtained for frequency (ωn) in this system is ωn2 =k/m, what is the natural frequency?arrow_forwardA machine weighing 10kN is supported on its foundation by spring mounting. the piston of the machine moves up and down with a harmonic frequency 10 cycles per second. The piston has a weight of 500N and total stroke of 500mm. Determine the maximum force transmitted to the foundation if the total spring stiffness k = 5N/mm. Ignore damping.arrow_forwardDetermine the differential equation of motion for the double pendulum shown in terms of12anduu where 12u and u are the horizontal distances of the masses from the leftmost verticalline that makes angle 1 from it. Find the natural frequencies, the ratios of the amplitudes, and thelocation of the nodes for the two modes of vibration. Assume m1=m2=m, and l1 =l2 = l=arrow_forward
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