Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.2, Problem 33P
To determine
The natural period of vibration of the wheel
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The 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.
The 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.
The uniform beam is supported at its ends by two springs
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Ok k = 305 N/m and mB
Ok
k = 408 N/m and mB
k = 609 N/m and mB = 2
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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 system is at rest with the sprng unstretched when theta = 0. The 5.3 kg uniform slender bar is then given a slight clockwise nudge. The value of b is 0.45 m. If the bar comes to momentary rest when theta = 58, determine the spring constat k. For the value k = 65N/m, find the magnitude of the angular velocity of the bar when theta = 38arrow_forwardThe wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration ke=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k-2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 8=0°. The spring's length at the state 2 is L2=4 m. (6) The elastic potential energy the state 2 is HILAI L₂ # State 2 ZG State 1 (N-m) (two decimal places)arrow_forwardThe wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration ke=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k-2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 0=0°. The spring's length at the state 2 is L2=4 m. (4) The elastic potential energy at the potion 1 is_ HULKU 2₂ State 2 G m State 1 (N-m) (two decimal places)arrow_forward
- 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. Given Required Solutionarrow_forwardThe linkage consists of two 4-kg rods AB and CD and a 18-kg bar BD. Rod CD is subjected to a couple moment M = 16 Nxm. When 0 = 0°, rod AB is rotating with an angular velocity w = 3 rad/s. I=1.9m B e 0 roo 2 D M Find the angular velocity w when = 52deg. Give your answer with 2 decimals.arrow_forwardThe wheel is attached to the spring. The mass of the wheel is m=20 kg. The radius of the wheel is 0.6m. The radius of gyration ke=0.4 m. The spring's unstretched length is Lo=1.0 m. The stiffness coefficient of the spring is k=2.0 N/m. The wheel is released from rest at the state 1 when the angle between the spring and the vertical direction is 8-30°. The wheel rolls without slipping and passes the position at the state 2 when the angle is 8=0°. The spring's length at the state 2 is L2=4 m. (3) The stretched spring length of the spring at the state 1 is_ places) 2₂ State 2 7717 State 1 _(m) (two decimalarrow_forward
- 22-33. If the 20-kg wheel is displaced a small amount and released, determine the natural period of vibration. The radius of gyration of the wheel is kg = 0.36 m. The wheel rolls without slipping. k = 500 N/m ww. 0.5 marrow_forward22–33. If the 20-kg wheel is displaced a small amount and released, determine the natural period of vibration. The radius of gyration of the wheel is kG = 0.36 m. The wheel rolls without slipping. k = 500 N/m 0.5 marrow_forwardThe wheel has a mass of 25 kg and a radius of gyration kb = 0.15m. It is originally spinning at @=40 rad/s. If it is placed on the ground, for which the coefficient of kinetic friction is uc = 0.5, determine the time required for the motion to stop. What are the horizontal and vertical components of reaction which the pin at A exerts on AB during this time? Neglect the mass of -0.4 m AB. 0.2 m- B 0.3 m Iarrow_forward
- 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.arrow_forwardImportant problem. The motor produces a counterclockwise torque 1 N.m on the attached disk A. A Part of this torque is transferred to the disk C through the belt after amplification. The disk A has mass 0.5 kg. and the disk C has mass = 4.5 kg. Find: (50 m 5omm pully C I. The difference tension between the palley A Te belt parts (7- T). II. The angular acceleration of the disk С. The angular acceleration of disk A. The angular velocity of the disk C after 5 seconds from the motion start. The transferred torque to the disk C. III. IV. V.arrow_forward3 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_forward
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