Engineering Mechanics: Dynamics (14th Edition)
14th Edition
ISBN: 9780133915389
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 22.6, Problem 73P
To determine
The differential equation that describes the motion in terms of the angle of the bars rotation and the damping coefficient of the dashpot.
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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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- A block-spring system has a maximum restoring force Fmax = 0.1 N. If the amplitude of the motion is A = 0.16 m and the mass of the block is %3D m 100 g then the angular frequency w is equal toarrow_forwardDetermine the equivalent torsional spring constant of a spring that will represent the system such that this torsional spring will be located at where the given bar turns. k=5N/m and l=1.5meters (answer in N- m) * 4 = k = k kz = 2k k3 = 3k F x lenarrow_forwardA 64-lb weight suspended from a spring (spring constant is 200 lb/ft) is released from rest 0.4 ft below the equilibrium position. If there is a resistance (lb) numerically equal to 0.04 times the velocity at any instant, determine the time for the damping factor to decrease 50% of its initial value g=32 ft/sec squarearrow_forward
- 4.A spring with a constant of 180 N/m connected to a 5 kg load is in equilibrium. Then the object is pulled 0.2 m and given an initial velocity of 1 m/s in the direction opposite to the direction of attraction. If the force external acting satisfies the function F(x) = 360x and the damping force is ignored. Determine the problem of the position of the object at any time.arrow_forwardCritical damping means a situation in which the vibrator returns from the extreme position to the equilibrium position as quickly as possible so that the body does not pass over the equilibrium position. If the characteristic frequency of the body is 1.85 Hz and the mass is 590 kg, what is the damping coefficient of the suspension in the case of critical damping? Enter the answer in whole numbers.arrow_forwardA mass of a 2 slug, when attached to a spring, causes an elongation of 2 ft in this spring and then comes to rest in the equilibrium position. Starting at t = 0 an external force equal to f(t) = 8 (sin (4t)) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force equal to 8 times the instantaneous velocity.arrow_forward
- The 8-kg body is moved 0.2 m to the right of the equilibrium position and released from rest at time t = 0. Determine its displacement at time t = 2 s. The viscous damping coefficient e is 20 N-s/m, and the spring stiffness k is 32 N/m. 8 kg ww k Equilibrium position mg cx = 20x kx = 32x-arrow_forwardDetermine the value of the damping coeffecient c for which the system is critically camped if k = 76 kN/m and m = 124kgarrow_forwardWhen a mass of 2 kilograms is attached to a spring whose constant is 32 N/m, it reaches rest in the equilibrium position. Starting at t = 0, a force equal to f(t) = 68(e^-2t)cos4t is applied to the system. Determine the equation of motion in the absence of damping.arrow_forward
- Question 1 In order to reduce vibrations being transmitted to the floor, a machine of mass m = 150kg is supported on 4 helical steel springs together with 4 dashpots which all act in parallel with each other. The stiffness of each spring is given by k1= 3.7 MN/m, and the damping coefficient of each dash-pot is given by c1 = 6.1kNs/m. To test how well the isolation system works, the machine is turned off and a shaker that produces a driving force of 100N at a frequency of 65 Hz is attached to the machine, causing it to vibrate. The mass of the shaker is negligible compared to the mass of the machine. Use a phasor diagram to determine: The displacement amplitude X of the machine, The phase angle by which the driving force leads the displacement.arrow_forwardTwo blocks A and B, each of mass m , are supported as shown by three springs of the same constant k Block A and B are connected by a dashpot and block B is connected to the ground by two dashpots, each dashpot having the same coefficient of damping c Block A is subjected to a force of magnitude P=Pm sin wf t. Write the differential equations defining the displacements xA and xB of the two blocks from their equilibrium positions.arrow_forwardA mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at t = 0, an external force equal to f(t) = 2sin(4t) is applied to the system. Find the equation of motion if the surrounding medium offers a damping force that is numerically equal to 8 times the instantaneous velocity. Hint: Use g = 32 ft/s2 for the acceleration due to gravity.arrow_forward
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