Engineering Mechanics: Dynamics, Student Value Edition (14th Edition)
14th Edition
ISBN: 9780134082424
Author: HIBBELER, Russell C.
Publisher: PEARSON
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Chapter 22.6, Problem 42P
To determine
The equation which describes the position of the block as a function of time.
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The 35-lb block is attached to two springs having a stiffness of k = 14 lb/ft . A periodic force F=(8cos3t)lb, where t is in seconds, is applied to the block.
Determine the maximum speed of the block after frictional forces cause the free vibrations to dampen out.
A spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its equilibrium position and given a downward velocity of 1.50 ms, determine the differential equation which describes the motion. Assume that positive displacement is downward. Also
determine the position of the block when t = 0.22 s. (Show free-body diagram of the system.)
A 9-kg block is suspended from a spring having a stiffness of k = 200 N/m. If the block is given an upward velocity of 0.4 m/s when it is 95 mm above its equilibrium position, determine the equation which describes the motion. Assume that positive displacement is downward.
Chapter 22 Solutions
Engineering Mechanics: Dynamics, Student Value Edition (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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- A two degrees of freedom mass spring system is fixed at one end, where independent masses can move only in the vertical direction. Considering the system as finite elements, determine the vertical displacement for each mass. Also draw the free body diagram of this system. Use 'X' KN/m as the stiffness value for all the springs and 'Y' Kg as the value for all masses. Where, 'X'= (63) 'Y'= (93)arrow_forwardA 4-lb weight is attached to a spring having a stiffness k = 10 lb/ft The weight is drawn downward a distance of 4 in. and released from rest. If the support moves with a vertical displacement in , where t is in seconds, determine the equation which describes the position of the weight as a function of time.arrow_forwardA spring is stretched 200 mm by a 15-kg block. If the block is displaced 200 mm downward from its equilibrium position and given a downward velocity of 0.75 m/s, determine the equation which describes the motion. Assume that positive displacement is downward.arrow_forward
- The 25-lb block is attached to two springs having a stiffness of k = 14 lb/ft . A periodic force F=(8cos3t)lb, where t is in seconds, is applied to the block. Determine the maximum speed of the block after frictional forces cause the free vibrations to dampen out. Express your answer to three significant figures and include the appropriate units.arrow_forwardA 9-kg block is suspended from a spring having a stiffness of k = 200 N/m. If the block is given an upward velocity of 0.4 m/s when it is 95 mm above its equilibrium position, determine the maximum upward displacement of the block measured from the equilibrium position. Assume that positive displacement is downward.arrow_forwardAn 8-kg block is suspended from a spring having a stiffness k = 80 N/m. If the block is given an upward velocity of 0.4 m/s when it is 90 mm above its equilibrium position, determine the equation which describes the motion and the maximum upward displacement of the block measured from the equilibrium position. Assume that positive displacement is measured downward.arrow_forward
- A 2-kg block is suspended from a spring having a stiffness of 800 N/m. If the block is given an upward velocity of 4 m/s when it is displaced downward a distance of 150 mm from its equilibrium position, determine the equation which describes the motion. Assume that positive displacement is downward.arrow_forwardThe rubber mallet is used to drive a cylindrical plug into the wood member. If the impact force varies with time as shown in the plot, determine the magnitude of the linear impulse delivered by the mallet to the plugarrow_forwardA 4 kg mass suspended from a spring having stiffness of k= 600N/m. if the block is pushed50mm upward from its equilibrium position and then released from rest dertermine the equation which describes the blocks motionarrow_forward
- A spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its equilibrium position and given a downward velocity of 1.50 m/s,determine the differential equation which describes the motion. Assume that positive displacement is downward.Also, determine the position of the block when t = 0.22 s.arrow_forwardThe conveyor belt is moving downward at 5 m/s. If the coefficient of static friction between the conveyor and the 15-kg package Bis * mu_{x} = 0.62 , determine the shortest time the belt can stop so that the package does not slide on the beltarrow_forwardThe semicircular bar is smooth. The unstretched length of the spring is 0.250 m. The 6-N collarat A is given a downward velocity of 4 m/s, and when it reaches B the magnitude of its velocity is 12 m/s.Determine the spring constant k.arrow_forward
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Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license