Engineering Mechanics Dynamics
14th Edition
ISBN: 9780133976717
Author: HIBBELER, Russell C.
Publisher: Pearson Education
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Chapter 22.6, Problem 69P
To determine
Show that if the damping coefficient
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Determine the steady-state amplitude of the mass center of the bar of Fig P6.3 when its right end is subject to a moment M=4000son105t N.m.
The block shown is depressed 1.2 in. from its equilibrium position and released. Knowing that after 10 cycles the maximum displacement of the block is 0.5 in., determine (a ) the damping factor c/c,(b) the value of the coefficient of viscous damping. (Hint: See Problems 19.129 and 19.130.)
The mass of a single degree damped vibrating system is 7.5 kg and makes 24 free oscillations in 14 seconds when disturbed from its equilibrium position. The amplitude of vibration reduces to 0.25 of its initial value after five oscillations. Determine : 1. stiffness of the spring, 2. logarithmic decrement, and 3. damping factor, i.e. the ratio of the system damping to critical damping.
Chapter 22 Solutions
Engineering Mechanics Dynamics
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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- for the system shown determine the natural frequency and the damping factorarrow_forwardA mass of 500 kg is mounted on supports having a total stiffness of 100 kN/m and which provides viscous damping, the damping ratio being 0.4. The mass is constrained to move vertically and is subjected to a vertical disturbing force of the type F cos ?t. Determine the frequency at which resonance will occur and the maximum allowable value of F if the amplitude at resonance is to be restricted to 5 mm.arrow_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_forward
- A body vibrating with viscous damping makes five complete oscillations per second, and in 10 cycles its amplitude diminishes by 1/5 of the orginal value. Determine the logarithmic decrement and the damping ratio.arrow_forwardThe system shown left composed by two rigid bars with a distributed mass of m and 2m, respectively. Determine the natural vibration period of the system. (k = 100 N/m,c = m = 10kg/m, L = 4m)arrow_forwardDetermine the steady-state amplitude of the mass center of the bar of Fig P6.3 when its right end is subject to a moment M=4000sin105t N.m. Expected answer X=0.988mmarrow_forward
- Two identical uniform bars are welded together at a right angle and are pivoted about a horizontal axis through point O as shown. Determine the critical driving frequency of the block B which will result in excessively large oscillations of the assembly. The mass of the welded assembly is m.arrow_forwardA three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a known weight at a known distance from the axis of rotation and to measure the frequency of oscillations after releasing it from rest with a small initial angle. In this case, a weight of Wadd = 50 lb is attached to one of the blades at a distance R = 20 ft from the axis of rotation. Knowing that when the blade with the added weight is displaced slightly from the vertical axis, and the system is found to have a period of 7.6 s, determine the centroidal mass moment of inertia of the three-blade rotor.arrow_forwardFor a certain mass-spring system m = 100 kg and k = 8000 N/m. Determine the value of the critical damping constant C_c and the damped natural frequency W_d and the logarithmic decrement d if C = C_c/3arrow_forward
- 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_forwardShow that in the case of heavy damping (c>cc ), a body released from an arbitrary position with an arbitrary initial velocity cannot pass more than once through its equilibrium position.arrow_forward1. 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_forward
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