*22-76. Determine the differential equation of motion for the damped vibratory system shown. What type of motion occurs? Take k = 100 N/m, c = 200 N-s/m, m = 25 kg.
Q: A 10-kg block is suspended from a cord wrapped around a 5-kg disk, as shown in Fig. 22-10a. If the…
A: Given The mass of the block is mb=10 kg. The mass of the disk is md=5 kg. The stiffness of the…
Q: 22-39. The slender rod has a weight of 4 lb/ft. If it is supported in the horizontal plane by a…
A: Given: The weight of rod per unit length, w = 4 lb/ft The sketch for the rod and string for a…
Q: 22-47. The uniform rod has a mass of m. If it is acted upon by a periodic force of F = F, sin wi,…
A: Consider the diagram shown below for the given spring-mass system.
Q: e amplitude
A: given:k=64.4lbk=54lb/in
Q: own below is of mass m and length L. Determine the displacement transmissibility (0/ Y). C mass (m)
A: Vibratory systems include mechanisms for storing potential energy (springs), kinetic energy…
Q: Magnitude of 23N harmonic force is acting on an undamped system with mass of 10kg and stiffness of…
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Q: 22-33. If the 20-kg wheel is displaced a small amount and released, determine the natural period of…
A: Given: The mass of the wheel, m = 20 kg The radius of the gyration, KG = 0.36 m The spring…
Q: Assuming that the gyroscope is at a point on the Earth's surface with latitude A and that ws >> 7,…
A: GYROSCOPE If the axis of spinning of rotating body is given and angular motion about an axis of spin…
Q: Determine the differential equation of motion and establish the critical damping for the system…
A: Draw the motion diagram of the system.
Q: 22-73. The bar has a weight of 6 lb. If the stiffness of the spring is k = 8 lb/ft and the dashpot…
A: Given data To determine 1) The differential equation which describes the motion in terms of angle…
Q: O(+ 3r The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small…
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Q: 22-23. The 20-kg disk, is pinned at its mass center O and supports the 4-kg block A. If the belt…
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Q: 22-51. The 40-kg block is attached to a spring having a stiffness of 800 N/m. A force F = (100 cos…
A: The natural frequency of vibration of the system is The forced frequency is The amplitude of the…
Q: *22-24. The 10-kg disk is pin connected at its mass center. Determine the natural period of…
A: Given Mass of the disk = 10 kg Spring constant = 80 N/m Diameter of the disk = 150 mm = 0.15 m To…
Q: 22-11. While standing in an elevator, the man holds a pendulum which consists of an 18-in. cord and…
A: Given Data: Length of cord is L = 18 in. Mass of bob is m = 0.5 lb. Acceleration of lift of lift is…
Q: 22-21. If the wire AB is subjected to a tension of 20 lb, determine the equation which describes the…
A: Using Newton’s laws of motion equation for horizontal motion, On substituting values we get,
Q: A cas have M = 1000 kg, eppective stiptness of sPoing 200 kN/ if it is dõiven along Bough doad that…
A: The mass and stiffness of the car body is given Mass (m) =1000kg Stiffness (k)=200kN/m = 200000N/m…
Q: *22-40. If the slender rod has a weight of 5 lb, determine the natural frequency of vibration. The…
A: Give a disturbance of small angle θ radian in the anticlockwise sense to the given bar as shown in…
Q: 22-49. The light elastic rod supports a 4-kg sphere. When an 18-N vertical force is applied to the…
A: Given, Mass (m) = 4 kg Froce (F) = 18 N Δy = 14 mm=0.014 δ0 = 15 mm Harmonic frequency (ω0 )= 2 Hz…
Q: *22-68. The 200-lb electric motor is fastened to the midpoint of the simply supported beam. It is…
A: Write the expression for the stiffness of the beam. Write the expression for the natural frequency…
Q: *22-16. A block of mass m is suspended from two springs having a stiffness of ki and k2, arranged a)…
A: Given: The mass of the block is m. The stiffness of the two springs is k1 and k2. Part (a) The…
Q: *22-12. Determine the natural period of vibration of the uniform bar of mass m when it is displaced…
A: Consider the diagram shown below for the small angular displacement of the rod.
Q: 22-29. The plate of mass m is supported by three symmetrically placed cords of length I as shown. If…
A: The tension in each rod is equal as the cords are placed symmetrically. Draw a free body diagram…
Q: 22-18. The uniform beam is supported at its ends by two springs A and B, each having the same…
A: Given, Mass of the beam (mB) = 50 kg "k" is the stiffness of the spring Time Period(T1) = 0.83 s The…
Q: *22-20. A uniform board is supported on two wheels which rotate in opposite directions at a constant…
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Q: 22-35. Determine the natural period of vibration of the 3-kg sphere. Neglect the mass of the rod and…
A: The free-body diagram of the mass is given as, CD is fix postion and AB is a position at an angle θ…
Q: *22-28. The platform AB when empty has a mass of 400 kg. center of mass at G1, and natural period of…
A: Write the given data: mp=400kgmc=1.2 Mg=1200 kg1000 kg1 Mgl1=2.50 ml2=1.83 mτ1=2.38 sτ2=3.16 s
Q: 22-37. The disk has a weight of 30 lb and rolls without slipping on the horizontal surface as it…
A: Given: The weight of the disc, w = 30 lb The angle turned by disc, θ = 0.2 rad The stiffness of the…
Q: 22-75. A bullet of mass m has a velocity v, just before it strikes the target of mass M. If the…
A: Given: mass of the bullet =m Mass of the target = M velocity of bullet = v0 bullet is embeds on the…
Q: 22-22. The bar has a length I and mass m. It is supported at its ends by rollers of negligible mass.…
A: Determine the moment of inertia about point O.
Q: 22-69. Two identical dashpots are arranged parallel to each other, as shown. Show that if the…
A: Free body diagram of the system in equilibrium and disturbed condition is, In statics equilibrium,…
Q: 22-71. If the amplitude of the 50-lb cylinder's steady-state vibration is 6 in., determine the…
A: Amplitude of vibration A =6 in k = 200 lb/ft c = 25 lb s/ ft m = 50 lb δ = 9 in ωn=keqm=2km=2.8284…
Q: A 9.1kg body is suspended from a spring of constant k = 2.0kN/m. At time t 0, it has a downward…
A: Mass of the body, m=9.1 kg Spring constant, k=2 kN/m. Here, frequency of the system is given by,…
Q: Determine the amplitude of the reaction at A for the beam loaded as shown. (X=0.1 m, x2=0.1 m, x30.4…
A:
Q: *22-36. If the lower end of the 6-kg slender rod is displaced a small amount and released from rest,…
A: Given: The mass of the slender is m=6 kg. The stiffness of the spring is k=200 N/m. The expression…
Q: In the system shown have modulus of rigidity G1 and G2, derive the differential equation of the…
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Q: 22-79. Draw the electrical circuit that is equivalent to the mechanical system shown. Determine the…
A: Relation between the electrical variables and the mechanical system is as follows: Mechanical…
Q: H. W- 2 Determine the natural frequency of the system shown beside.
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Q: 22-41. If the block-and-spring model is subjected to the periodic force F = F, cos wt, show that the…
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Q: When a 2-kg block is suspended from a spring, the block oscillates with a cyclic frequency of f = 45…
A:
Q: A 3.7kg body is suspended from a spring of constant k = 6.1kN/m. At time t = 0, it has a downward…
A: Given Mass, m = 3.7 kg Spring constant, k = 6.1 kN/m Find System period,…
Q: Consider a mass-spring system with a mass of 1 kg attached to the spring, having spring constant 9…
A: given data;mass (m)=1kgspring constant k=9kg/mF(t)=4cosωt
Q: If the 20-kg wheel is displaced a small amount and released, determine the natural period of…
A: Vibration occurs when an elastic body, such as a spring, a beam, or a shaft, is moved from its…
Q: 22-57. The electric motor turns an eccentric flywheel which is equivalent to an unbalanced 0.25-lb…
A:
Q: A spring is stretched 200 mm by a 15-kg block. If the block is displaced 100 mm downward from its…
A: The SHM equation is my..+ky=0The general solutions of the above differential…
Q: 22-15. A platform, having an unknown mass, is supported by four springs, each having the same…
A: The expression of a time period t=2πmk
Q: 22–38. The machine has a mass m and is uniformly supported by four springs, each having a stiffness…
A: given: mass of machine=m stiffness of the given four spring=k
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- An electric motor with a mass of 20 kg is placed in the middle of a beam that is jointly connected on both sides. Rotor its unbalance is equivalent to a mass of 0.3 kg at a distance of 0.020 m from the axis of rotation. Due to the electric motor force acting on the beam t Sin F F 0 . The rotor is rotating at an angular speed of = 40 rad / sec. Engine under the influence of force Find the displacement amplitude at the point where it is located (in the middle). The beam mass will be neglected. The beam has a modulus of elasticity E = 200000000000 N / m2 (200 GPa).A 2kg mass is attached to a horizontal spring whose recuperative constant is k = 10 N / m. Separating the mass from the equilibrium position, the system begins to oscillate, if the amplitude is 5 cm. Determine: Your velocity and acceleration at 3.6 secondsA spring has a stiffness of 600 N/m, if a 4 kg block is attached to the spring, pushed 500 mm above its equilibrium position, and released from rest; determine the angular frequency. Assume the positive displacement is measured downward
- Determine the spring constant, k if the system is to oscillate with a natural frequency, f of 11 Hz. Mass = 36 kgAn 8-kgkg block is suspended from a spring having a stiffness k=80N/mk=80N/m. If the block is given an upward velocity of 0.4 mm // ss when it is 90 mmmm above its equilibrium position, determine the equation which describes the motion of the block measured from the equilibrium position. Assume that positive displacement is measured downward. Determine the maximum upward displacement of the block measured from the equilibrium position. Assume that positive displacement is measured downward.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.
- 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 load weighing 2 kg is attached to a spring. If the damping force is 5.5, spring constant is 4.2, and external force is sin(t), and the load is released from rest 0.2 inches below its equilibrium, determine the displacement of the object at any time t.It is desired to adjust the damping of the passenger car's suspension so that the vibration is damped to one tenth of the original during one oscillation. Based on this, determine the relative attenuation constant D (give the answer to two decimal places). The car has a mass of 1500 kg and the body frequency is 1.32 Hz.
- The following vibration system oscillates with a small angle. x = 0.6m, y = 1.8m, k = 18N/m. From the motor: static deflection = 0.2m, forcing frequency = 30 rad/s. If the starting angle from rest is 2 radians (counter-clockwise) and mass A is 10 kilograms, determine: 1. The natural frequency in radians per second. 2. The natural period in second 3. The amplitude of free vibration in meters (reference: neutral position of the spring below), 4. The amplitude of steady-state vibration in meters (reference: neutral position of the spring below) 5. The magnification factor 6. The overall displacement in meters when t= 1 second (reference: neutral position of the spring below).1- A particle is in simple harmonic motion. It hasa velocity of 5m/s when it is 2 m from its staticequilibrium position and has a velocity of 3.5m/s when it is 3m from the equilibriumposition. Determine amplitude , time period,maximum acceleration and the frequency ofvibration.A mass of 0.75kg is attached to one end of a horizontal spring, of spring constant 400Nm-1. The other end of the spring is attached to a regid wall. The mass is pushed so that at time t=0 it is 4.0cm closer to the wall than the equilibrium position and is traveling towards the wall with a velocity of 0.50ms-1. a) determine the total energy of the oscillating system. b) obtain an expression for the displacement of the mass in the form x=Acid(wt+π)m, giving numerical values for A, w and phi