22-22. The bar has a length I and mass m. It is supported at its ends by rollers of negligible mass. If it is given a small displacement and released, determine the natural frequency of vibration. B.
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: 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: 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: The 0.2 kg mass is suspended from a rigid frame. Pin A at the end of arm OA engages a slot in the…
A: Given:m=0.2 Kgω=35 rad/sk=310 N/m
Q: AD Point A is connected to a spring to maintain the bar in vertical direction, and th stiffness k =…
A: The mass of the uniform bar AB is given as,m=8 kg The length of the uniform bar AB is given as,…
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: The system is in equilibrium in the position. Find the period of vibration for small amplitudes.…
A: Given data: k=75 N/mm=1.8 kg Need to determine the period of vibration for small amplitudes.
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: 22-73. 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: 22-23. The 20-kg disk, is pinned at its mass center O and supports the 4-kg block A. If the belt…
A:
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: 1. The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m') vibrates in…
A: E – the material Young's modulus, I – the moment of inertia, ρ – the material density, A – the area…
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: 22-46. A 5-kg block is suspended from a spring having a stiffness of 300 N/m. If the block is acted…
A:
Q: A 30-lb uniform cylinder can roll without sliding on a 15° incline. A belt is attached to the rim of…
A: The data given is,
Q: 1. The uniform rod ABC weighs 5 lb, and is attached to wo springs as shown. If end C is given a…
A:
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: 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: 22-49. 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: k2 k3 m - 13-
A:
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: 22–13. The body of arbitrary shape has a mass m, mass center at G, and a radius of gyration about G…
A: Write the expression for the moment about point O. However, for small rotation sinθ=θ, hence the…
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…
A:
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: 22-69. 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 12.4 kg block is suspended from a cord wrapped around a 6.4 kg disk as shown in the figure. If the…
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: 22-41. If the block-and-spring model is subjected to the periodic force F = F, cos wt, show that the…
A:
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: 22–10. The uniform rod of mass m is supported by a pin at A and a spring at B. If B is given a small…
A: Given data: The mass of rod is, m. Draw the free body diagram of the rod with all the parameters.
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: machine mounted on elastic supports, is free to vibrate vertically. The machine has a mass of 40 kg…
A: mass of machine, M=40kgunbalancing mass, m=2kgeccentricity, e=150mmResonance speed, Nn=621rpm…
Q: 22-57. The electric motor turns an eccentric flywheel which is equivalent to an unbalanced 0.25-lb…
A:
Q: A 3-kg block is suspended from a spring having a stiffness of k = 200 N/m. If the block is pushed 50…
A: Givenk=200N/mm=3 kgx==50 mm=0.05mAngular frequency is given asω=kmω=2003ω=8.16 rad/sec
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
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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.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.If k = 23 kip/in and W = 329 kip, determine the period of vibration in seconds.
- While 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.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/mDetermine the natural period of vibration of the uniform bar of mass m when it is displaced downward slightly and released.
- 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 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 SolutionIf both springs are usntretched when the mass is in the central position shown, determine the static deflection of the mass. What is the period of oscillatory motion about the position of static equilibrium? The mass m = 3.4, the spring constant k = 295 N/m, and the angle theta = 31 degrees
- 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.When a free vibrations is run on the system, the ratio of amplitudes on successive cycles is 2.5 to 1.  determine the response of the machine due to a rotating unbalance of 0.25 kg*m when the machine operates at 2000 Rev/min.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