22-47. The uniform rod has a mass of m. If it is acted upon by a periodic force of F = F, sin wi, determine the amplitude of the steady-state vibration. F= Fo sin wt
Q: consists a with a weight of 400 2000 lb/in. By testing the system, it was found that a force of 200…
A: As per guidelines we can answer only the first three parts kindly post the remaining parts in…
Q: *22-76. Determine the differential equation of motion for the damped vibratory system shown. What…
A: Write the expression of the equivalent spring stiffness.
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: 8(s+5) Y(s) s'+10s +16s +40 vibration of the mass m caused by the displacement of the foundation,…
A: 8×s+5s3+10s2+16s+40×0.05s3+5 X(s) is given above plot of response -
Q: e amplitude
A: given:k=64.4lbk=54lb/in
Q: The homogeneous beam has a mass of 3m and supported at point B. For small oscillations, determine…
A: given mass of the rod = 3mtotal length of the rod L= 4Lspring constant of spring 1= 2Kspring…
Q: A 3 kg mass suspended from a spring having stiffness of k= 200N/m. if the block is pushed 50mm…
A: Let us draw the mass-spring system General solutions of that differential equation Hence the…
Q: The uniform beam is supported at its ends by two springs A and B, each having the same stiffness k.…
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Q: The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m') vibrates in lengthwise…
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Q: 22–25. If the disk in Prob. 22-24 has a mass of 10 kg, determine the natural frequency of vibration.…
A: The mass of the disc is m=10 kg. The spring constant of the spring is k=80 N/m. The radius of the…
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: *22-60. The 450-kg trailer is pulled with a constant speed over the surface of a bumpy road, which…
A: Given data: The mass of the trailer, m = 450 kg. The amplitude is, A = 50 mm. The wavelength is, λ…
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: 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: 22-49. 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: 3 m 1 m 1 m
A: Given, w=120N/m
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: 22-69. 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: *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: Q2-A shaft of length 0.75 m, supported freely at the ends, is carrying a body of mass 90 kg at 0.25…
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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…
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Q: *22-56. The small block at A has a mass of 4 kg and is mounted on the bent rod having negligible…
A: Given, Mass of block A, m=4 kg Length of the horizontal arm of the rod, L1=0.6 m Length of the…
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…
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Q: 22–17. The 15-kg block is suspended from two springs having a different stiffness and arranged a)…
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Q: tiffness 250 Nm'. The rotor is unbalanced such that the quivalent to a mass of 5 kg located 50 mm…
A: data provided m = 40 kg me = 5 kg e = 50 mm =0.05m ς = 0.15w = 1000 rpm =1000×2π60= 104.72 rad/s
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: Determine the natural period of vibration of the pendulum if it is given a small displacement and…
A: This is a physical pendulum
Q: When a 2-kg block is suspended from a spring, the spring is stretched a distance of 40 mm. Determine…
A: To find : The period of vibration for a 0.5 kg block attached for the same spring. Given : The…
Q: f(t) www
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Q: Determine the natural frequency fn of vertical oscillations of the cylinder of mass m. The mass and…
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Q: Determine the natural frequency Wn of vertical oscillations of the cylinder of mass m. The mass and…
A: Answer: The correct answer is option (b).
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
Q: The amplitude of vibration of an undamped system is measured to be 1 mm. The phase shift from t = 0…
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Q: A 12.6 kg block is suspended from a cord wrapped around a 6.6 kg disk as shown in the figure. If the…
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- 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.If k = 23 kip/in and W = 329 kip, determine the period of vibration in seconds.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.
- 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/mWhile 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/s2, determine the natural period of vibration for small amplitudes of swing.The engine of the helicopter is delivering 600 hp to the rotorshaft when the blade is rotating at 1200 rpm. Determine to thenearest 1/8 in the diameter of the shaft is the allowable shearstress is 10.5 ksi and the vibration limits the angle of twist ofthe shaft to 0.05 rad. The shaft is 2 ft long and made fromsteel.
- 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 SolutionAn 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 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
- A smooth disk with a mass of 3 kg is placed on a cylindrical surface.It can move without slipping. This cylinder has a mass of 2 kgproperly connected to the AB bar at its midpoint. AB bar is also middleIt is connected to a spring with a constant k = 300 N/m. EUrod can move freely around point A. Boccurs when the tip is given a small displacement and released.Calculate the period of the vibration.Assuming that the L-shaped bar has negligible mass and in the equilibrium position shown, determine the natural period of vibration of the system by using A.) Kinematic equations a. I= 0.218 s b. T = 0.374 s c. T = 0.419 s d. T= 0.536 S B.) Energy method a. T = 0.218 s b. T= 0,374 s C. T = 0,419 s d. I= 0.536 S Given data: k = 200 N/m; h= 150 mm; m= 2 kg d= 100 mmThe 42-kg block is attached to a spring having a stiffness of k = 700 N/m . A force F=(100cos2t)N, where t is in seconds is applied to the block. Determine the maximum speed of the block for the steady-state vibration.