Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.1, Problem 12P
Determine the natural period of vibration of the uniform bar of mass m when it is displaced downward slightly and released.
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Chapter 22 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 22.1 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22.1 - A spring has a stiffness of 800 N/m. If a 2-kg...Ch. 22.1 - Prob. 3PCh. 22.1 - Prob. 4PCh. 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 - While standing in an elevator, the man holds a...Ch. 22.1 - Determine the natural period of vibration of the...Ch. 22.1 - Prob. 13PCh. 22.1 - Prob. 14PCh. 22.1 - Prob. 15PCh. 22.1 - Prob. 16PCh. 22.1 - Prob. 17PCh. 22.1 - The uniform beam is supported at its ends by two...Ch. 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 - Prob. 23PCh. 22.1 - Prob. 24PCh. 22.1 - If the disk in Prob. 22-24 has a mass of 10 kg,...Ch. 22.1 - A flywheel of mass m which has a radius of...Ch. 22.1 - Prob. 27PCh. 22.1 - The platform AB when empty has a mass of 400 kg...Ch. 22.1 - The plate of mass m is supported by three...Ch. 22.2 - Prob. 30PCh. 22.2 - Prob. 31PCh. 22.2 - Prob. 32PCh. 22.2 - If the 20-kg wheel is displaced a small amount and...Ch. 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 - A block which has a mass m is suspended from a...Ch. 22.6 - A 4-lb weight is attached to a spring having a...Ch. 22.6 - A 4-kg block is suspended from a spring that has a...Ch. 22.6 - Use a block-and-spring model like that shown in...Ch. 22.6 - A 5-kg block is suspended from a spring having a...Ch. 22.6 - The uniform rod has a mass of m. If it is acted...Ch. 22.6 - Prob. 48PCh. 22.6 - The light elastic rod supports a 4-kg sphere. When...Ch. 22.6 - Find the differential equation for small...Ch. 22.6 - Prob. 51PCh. 22.6 - Prob. 52PCh. 22.6 - The fan has a mass of 25 kg and is fixed to the...Ch. 22.6 - In Prob. 22-53 , determine the amplitude of...Ch. 22.6 - Prob. 55PCh. 22.6 - Prob. 56PCh. 22.6 - Prob. 57PCh. 22.6 - Prob. 58PCh. 22.6 - Prob. 59PCh. 22.6 - Prob. 60PCh. 22.6 - Prob. 61PCh. 22.6 - Prob. 62PCh. 22.6 - Prob. 63PCh. 22.6 - Prob. 64PCh. 22.6 - Prob. 65PCh. 22.6 - Determine the magnification factor of the block,...Ch. 22.6 - Prob. 67PCh. 22.6 - The 200-lb electric motor is fastened to the...Ch. 22.6 - Prob. 69PCh. 22.6 - Prob. 70PCh. 22.6 - If the amplitude of the 50-lb cylinder's...Ch. 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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- A large industrial cooling system of mass 160 kg is supported by six springsarranged in parallel. Two of the springs have equal stiffness of 30 kN/m, twohave stiffness of 15 kN/m, and the remaining two have stiffness of 10 kN/m.Determine:i) the total stiffness of the spring system;ii) the natural frequency of vibration of the motor;iii) the periodic time for the vibration.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.arrow_forwardThe 23-kg disk, is pinned at its mass center O and supports the 3-kg block A. The belt which passes over the disk is not allowed to slip at its contacting surface. Determine the natural period of vibration of the system.arrow_forward
- A motor weighing 400 lb is supported by springs having a total constant of 1200 lb/in. The unbalance of the rotor is equivalent to a 1-oz weight located 8 in. from the axis of rotation. Determine the range of allowable values of the motor speed if the amplitude of the vibration is not to exceed 0.06 in.arrow_forwardWhile standing in an elevator, the man holds a pendulum which consists of an 18-in. cord and a 0.5-lb bob. If the elevator is descending with an acceleration a = 4 ft/s2, determine the natural period of vibration for small amplitudes of swing.arrow_forwardDetermine the characteristic equation and the periods of vibration of the indicated system.arrow_forward
- The 23-kgkg disk, is pinned at its mass center OO and supports the 5-kgkg block AA. The belt which passes over the disk is not allowed to slip at its contacting surface. Determine the natural period of vibration of the system.arrow_forwardA 2-lb weight is suspended from a spring having a stiffness k = 2 lb/in. If the weight is pushed 1 in. upward from its equilibrium position and then released from rest, determine the equation which describes the motion. What is the amplitude and the natural frequency of the vibration?arrow_forwardThe system is in equilibrium in the position. Find the period of vibration for small amplitudes. Neglect the mass of the rod and size of the 1.8 kg. mass. Given Required Solutionarrow_forward
- 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=4000sin105t N.m. Expected answer X=0.988mmarrow_forwardWhen a 2-kg block is suspended from a spring, the spring is stretched a distance of 40 mm. Determine the period of vibration for a O.5-kg block attached to the same spring.arrow_forwardA 15-lb slender rod AB is riveted to a 12-lb uniform disk as shown. A belt is attached to the rim of the disk and to a spring that holds the rod at rest in the position shown. If end A of the rod is moved 0.75 in. down and released, determine (a) the period of vibration, (b) the maximum velocity of end A.arrow_forward
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