PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 22, Problem 24P
To determine
The natural period of vibration of the disk.
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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.
The 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.
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The 0.2 kg mass is suspended from a rigid frame. Pin A at the end ofarm OA engages a slot in the frame, causing the frame to oscillate in the verticaldirection as the arm turns. If the angular velocity of OA is ω=35 rad/s, determinethe amplitude of the steady-state vibration of the weight relative to the frame.
Chapter 22 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 22 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22 - A spring has a stiffness of 800 N/m. If a 2-kg...Ch. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - A 3-kg block is suspended from a spring having a...Ch. 22 - Prob. 10P
Ch. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Prob. 16PCh. 22 - Prob. 17PCh. 22 - A uniform board is supported on two wheels which...Ch. 22 - Prob. 24PCh. 22 - Prob. 30PCh. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Determine the differential equation of motion of...Ch. 22 - Prob. 36PCh. 22 - If the block-and-spring model is subjected to the...Ch. 22 - A block which has a mass m is suspended from a...Ch. 22 - A 4-lb weight is attached to a spring having a...Ch. 22 - A 4-kg block is suspended from a spring that has a...Ch. 22 - A 5-kg block is suspended from a spring having a...Ch. 22 - Prob. 48PCh. 22 - The light elastic rod supports a 4-kg sphere. When...Ch. 22 - Find the differential equation for small...Ch. 22 - Prob. 52PCh. 22 - The fan has a mass of 25 kg and is fixed to the...Ch. 22 - In Prob. 22-53 , determine the amplitude of...Ch. 22 - Prob. 55PCh. 22 - Prob. 56PCh. 22 - Prob. 57PCh. 22 - Prob. 58PCh. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 61PCh. 22 - Prob. 62PCh. 22 - Prob. 65PCh. 22 - Determine the magnification factor of the block,...Ch. 22 - Prob. 67PCh. 22 - The 200-lb electric motor is fastened to the...Ch. 22 - Prob. 70PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 79P
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- 3 m 1 m 1 m Determine the natural period of vibration of the pendulum if it is given a small displacement and released. Consider the two rods to be slender, each having a weight of 120 N/m.arrow_forwardThe uniform beam is supported at its ends by two springs A and B, each having the same stiffness k. When nothing is supported on the beam, it has a period of vertical vibration of 0.83 s. If a 50-kg mass is placed at its center, the period of vertical vibration is 1.52 s. Compute the stiffness of each spring and the mass of the beam. Ok k = 305 N/m and mB Ok k = 408 N/m and mB k = 609 N/m and mB = 2 n - - O10 11 11Ն ՆԱ B 1 = हarrow_forwardThe body of arbitrary shape has a mass m, mass center at G, and a radius ofgyration about G of . If it is displaced a slight amount from its equilibriumposition and released, determine the natural period of vibration.arrow_forward
- A smooth disk with a mass of 3 kg is placed on a cylindrical surface.It can move without slipping. This cylinder has a mass of 2 kgproperly connected to the AB bar at its midpoint. AB bar is also middleIt is connected to a spring with a constant k = 300 N/m. EUrod can move freely around point A. Boccurs when the tip is given a small displacement and released.Calculate the period of the vibration.arrow_forwardDetermine the natural frequency fn of vertical oscillations of the cylinder of mass m. The mass and friction of the stepped drum are negligible. 2r m k EVE k m 1 k m 1 2k m 2k marrow_forwardA machine of mass m is mounted on a vibration isolator as shown. If the foundation is vibrating according to p(t) = Psinot, where p(t) is the displacement of the foundation. Determine the motion transmissibility. The displacement x is measured from the equilibrium position in the absence of the vibration of the foundation. k₁ m b₂ k2 X m p(t) = P sin wtarrow_forward
- The block of mass m is suspended from three springs with stiffnessesk1 and k2 as shown. The frequency of vibration of this system is 5 Hz. Afterthe middle spring is removed, the frequency drops to 3.6 Hz. Determine theratio k2/k1arrow_forwardIf both springs are usntretched when the mass is in the central position shown, determine the static deflection of the mass. What is the period of oscillatory motion about the position of static equilibrium? The mass m = 3.4, the spring constant k = 295 N/m, and the angle theta = 31 degreesarrow_forwardm Base The response for the block is a sine harmonic function and its amplitude is 0.458 m The response for the block is a cosine harmonic function and its amplitude is 0.019 m The response for the block is a cosine harmonic function and its amplitude is 1.56 m The response for the block is a cosine harmonic function and its amplitude is 0.119 marrow_forward
- A coil of spring stiffness 4 N/mm supports vertically a mass of 20 kg at the free end. The motion is resisted by the oil dashpot. It is found that the amplitude at the beginning of the fourth cycle is 0.8 times the amplitude of the previous vibration. Determine the damping force per unit velocity. Also find the ratio of the frequency of damped 'and undamped vibrations.arrow_forwardThe uniform rod ABC weighs 5 lbf and is attached to wo springs as shown. If end c is given a small displacement and released, determine the frequency of vibration of the rod. Use Energy Method. k = 3 lby/in. k = 4 lbg/in. A 15 in. 15 in.arrow_forwardA block having a weight of 8 lb is suspended from a spring having a stiffness k = 40 Ib/ft. If the block is pushed y = 0.4 ft upward from its equilibrium position and then released from rest. What is the amplitude of the vibration? Assume that positive displacement is downwardarrow_forward
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