22-75. A bullet of mass m has a velocity v, just before it strikes the target of mass M. If the bullet embeds in the target, and the dashpot's damping coefficient is 0 < c << ce determine the springs' maximum compression. The target is free to move along the two horizontal guides that are “nested" in the springs.
Q: A mass of 1 kg, when attached to a spring, stretches it 2 m and then comes to rest in the…
A: Given: Mass of the body is 1 kg. Initial compression of the spring is 2 m. Force is, f(t) =…
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: A 1-lb weight stretches a spring 6 in., and the system is attached to a dashpot that imparts a…
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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: A mass weighing 8 pounds is attached to a spring whose constant is 4 lb/ft. The medium offers a…
A: The given data are: W=8 poundsk=4 lb/ftC=1 ftv=8 ft/s Here, W, k, C, and v represent the weight,…
Q: A mass weighing 8 lbs. stretches a spring 24 inches. Assuming that a damping force numerically…
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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: 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: If we attach an object weighing 8 lb to a spring, it stretched the latter by 1 ft. We attach a…
A: Given data: Here, Wso represents the weight of the object attached to spring, W represents the…
Q: O(+ 3r The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small…
A:
Q: A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a…
A:
Q: A mass weighing 2.45N stretches a spring 0.6125 meter. Assuming that a damping force numerically…
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: *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: The block (mass not given) is subjected to the force F = (501 sin(5.9t)) N, where t is in seconds.…
A:
Q: ) The 8kg body Figure 4 is moved 0.2m to the right of the equilibrium position and released from…
A: 'Since you have asked multiple questions, we will solve the first question for you. If you want any…
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: If you have the system shown, with mass m-120kg, stiffness kl-250 N/m, k2-50 N/m and damping…
A: Natural frequency: When a body is at rest, that is when no force is acting on the body, even though…
Q: 3. Determine the (a) system period and (b) the maximum velocity of the spring-mass system in ft/s if…
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Q: A small generator of mass m is supported by four anti- vibration springs to reduce vibration levels…
A: Given : m = 12 kg k = 800 N/m To find: Frequency of vibration and time period
Q: the constant of the support spring (without damping) which only transmits only up to 28% of the…
A: Drawing the figure for the given as shown below –
Q: and (b) the maximum
A: given:mass of block m=64.4 lbk=54lb/inA=3in
Q: A 2-kg mass is attached to a spring with spring constant 24 N/m. The system is then immersed in a…
A: Given:mass, m=2 kgspring constant, k=24 N/mβ= 16
Q: The 8kg body Figure 4 is moved 0.2m to the right of the equilibrium position and released from rest…
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: 22-35. 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: 10- The bar has a weight of 6 lb. If the stiffness of the spring is k = 8 lb/ft and the dashpot has…
A:
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: What is the natural frequency of the spring mass system shown below? The contact between the block…
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Q: Answer: a. A = b. t = k 500 N/m ÓT m = 20 kg
A:
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: 0(+) 31 0 The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small…
A:
Q: The mass of the system shown below is 10Kg. The mass is initially at rest when at time t=0, it is…
A: Given Data M=10 kg K=100 N/m c= 100 Ns/m
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: 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: equation
A: Assume mass m and spring constant k Newton second law of system md2xdt2+kx=f(t)d2xdt2+kxm=f(t)m now…
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: 4. If the frame in question 1(b) has a damping ratio of 10% and a fore P(t) = (1kN).sincot is…
A:
Q: A 2kg mass is attached to a horizontal spring whose recuperative constant is k = 10 N / m.…
A: Given data mass (m) = 2 kg spring constant (k) = 10 N/m Amplitude (A) = 5 cm = 0.05 m To determine…
Q: QI: A portion of an automobile suspension system consists of an elastic spring and a viscous damper,…
A:
Q: 3. A mass weighing 2.45N stretches a spring 0.6125 meter. Assuming that a damping force numerically…
A:
Q: 1 A-kg mass is attached to a spring with stiffness 40 N/m. The damping constant for the system is 4…
A:
Q: A mass weighing 5 pounds is attached to a spring whose constant is k = 7lb/tf. The medium offers a…
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Solved in 2 steps
- 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.If 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 degreesA mass weighing 5 pounds is attached to a spring whose constant is k = 7lb/tf. The medium offers a damping force that is foot numerically equal to the instantaneous velocity. The mass is released from a point 1 ft above the equilibrium position with a downward velocity of 8 ft/seg. Determine the equation of motion x(t) of this system
- 5. After a mass weighing 10 pounds is attached to a 5-foot spring,the spring measures 7 feet.This mass is removed and replaced with another mass that weighs 8pounds. The entire system isplaced in a medium that offers a damping force that is numerically equal to the instantaneousvelocity.a. Find the equation of motion if the mass is initially released from a point 1/2 foot belowthe equilibrium position with a downward velocity of 1 ft/s.b. Express the equation of motion in the form x(t) = Ae sin[( )t ]A mass weighing 8 pounds is attached to a spring whose constant is 4 lb/ft. The medium offers a damping force that is numerically equal to the two times instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 8 ft/s. (a) Specify the 2nd order DE as an IVP for the mass spring system.3. Determine the (a) system period and (b) the maximum velocity of the spring-mass system in ft/s if the spring was initially pulled 2.5 in. from equilibrium position and the amplitude was measured to be 3 in.
- When 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.A 50 kg dough machine is mounted on an elastic support and opera to a speed of 1000 rpm. It has an unbalanced mass of 2 kg at an eccentric distance of 0.1 meter. If the damping factor ℶ = 0.2, determine: a) the constant of the support spring (without damping) which only transmits only up to 28% of the unbalanced force to the foundation, b) the resonant frequency in rpm, and c) the magnitude of the force transmitted with the complete suspension d) Illustrate using graphicsA mass weighing 8 lbs. stretches a spring 24 inches. Assuming that a damping force numerically equally to 2 times the instantaneous velocity acts on the system, determine the position of the mass when it is initially released from equilibrium position with an upward velocity of 3 ft./s. after 1/4 secs.
- Solve for differential equations undetermined coefficients, do not go to international system A weight of 3.2Ib stretches a spring 6.4 ft. If the weight is released 3 inches below the equilibrium position with a downward directed speed of 6 ft/s and the mass-spring system is in the middle provides a damping force numerically equal to one fifth of the instantaneous speed, determine the equation of motion if an external force given by f(t) = e-t cos(2t) is also applied to weight.An 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 equivalent mass of a SDOF of 10 kg. The system has a natural frequency of 80 rad/s. The system is at rest in equilibrium when it is subject to a time dependent force. Determine and plot the response of the system if it is subject to a force of (a) 10 sin(40t)N, (b) 10 sin(80t) N, and (c) 10 sin(82t) N.