EP ENGR.MECH.:DYNAMICS-REV.MOD.MAS.ACC.
14th Edition
ISBN: 9780133976588
Author: HIBBELER
Publisher: PEARSON CO
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Chapter 22.1, Problem 12P
*22-12. 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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22–10. The uniform rod of mass m is supported by a pin
at A and a spring at B. If B is given a small sideward
displacement and released, determine the natural period of
vibration.
22-22. The bar has a length I and mass m. It is supported
at its ends by rollers of negligible mass. If it is given a small
displacement and released, determine the natural frequency
of vibration.
B.
22-23. The 20-kg disk, is pinned at its mass center O and
supports the 4-kg block A. If 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.
300 mm
k = 200 N/m
Chapter 22 Solutions
EP ENGR.MECH.:DYNAMICS-REV.MOD.MAS.ACC.
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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- 22–25. If the disk in Prob. 22-24 has a mass of 10 kg, determine the natural frequency of vibration. Hint: Assume that the initial stretch in each spring is do- k = 80 N/m 150 mm k = 80 N/marrow_forward22-39. The slender rod has a weight of 4 lb/ft. If it is supported in the horizontal plane by a ball-and-socket joint at A and a cable at B, determine the natural frequency of vibration when the end B is given a small horizontal displacement and then released. 0.75 ft 1.5 ftarrow_forward*22-24. The 10-kg disk is pin connected at its mass center. Determine the natural period of vibration of the disk if the springs have sufficient tension in them to prevent the cord from slipping on the disk as it oscillates. Hint: Assume that the initial stretch in each spring is ôo. k = 80 N/m /150 mm k = 80 N/m wwwarrow_forward
- 22-18. The 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. B.arrow_forward22-11. While 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/s, determine the natural period of vibration for small amplitudes of swing. a = 4 ft/sarrow_forward22-49. The light elastic rod supports a 4-kg sphere. When an 18-N vertical force is applied to the sphere, the rod deflects 14 mm. If the wall oscillates with harmonic frequency of 2 Hz and has an amplitude of 15 mm, determine the amplitude of vibration for the sphere. -0.75 marrow_forward
- 22-35. Determine the natural period of vibration of the 3-kg sphere. Neglect the mass of the rod and the size of the sphere. k = 500 N/m 300 mm -300 mmarrow_forward*22-56. The small block at A has a mass of 4 kg and is mounted on the bent rod having negligible mass. If the rotor at B causes a harmonic movement ôg = (0.1 cos 151) m, where t is in seconds, determine the steady-state amplitude of vibration of the block. -0.6 m- 1.2 m k = 15 N/marrow_forward22–13. The body of arbitrary shape has a mass m, mass center at G, and a radius of gyration about G of kg. If it is displaced a slight amount e from its equilibrium position and released, determine the natural period of vibration.arrow_forward
- 22-71. If the amplitude of the 50-lb cylinder's steady-state vibration is 6 in., determine the wheel's angular velocity w. 9 in. -c = 25 lb-s/ft k = 200 lb/ft k = 200 lb/ft Prob. 22-71 0000arrow_forward22-37. The disk has a weight of 30 lb and rolls without slipping on the horizontal surface as it oscillates about its equilibrium position. If the disk is displaced, by rolling it counterclockwise 0.2 rad, determine the equation which describes its oscillatory motion and the natural period when it is released. k = 80 lb/ft 0.5 ftarrow_forward*22-20. A uniform board is supported on two wheels which rotate in opposite directions at a constant angular speed. If the coefficient of kinetic friction between the wheels and board is u, determine the frequency of vibration of the board if it is displaced slightly, a distance x from the midpoint between the wheels, and released. Ex-| p- -p-arrow_forward
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