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Q: Determine the oscillations of a system with two degrees is L = (x² + y²) - w²(x² + y²)

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Q: pump has a specific speed of 45 and 600rpm when it delivers 0.01m3/s. Find the head developed by the…

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Q: The equilibrium position of the mass m = 3.8 kg occurs where y = 0 and YB = 0. When the attachment B…

A: Given data: mass of block (m) = 3.8 kg Spring stiffness (k) = 875 N/m

Q: (5) The uniform slender rod (mass m and length L) is pinned to the center of the uniform disk (mass…

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Q: 3. A light rod AB of length 600 mm has a fixed hinge at A and a mass of 5 kg concentrated at B. A…

A: The given information in the problem is shown in the following attached image:

Q: Two 40-g weights are attached at A and B to the rim of a 1.5-kg uniform disk of radius r = 100 mm.…

A: Consider the diagram shown below for the disc for a small angular displacement anticlockwise.

Q: 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: natural frequency of the system.

A: Given: A mass of 1 kg, m=1 kgAttached to two identical springs each of stiffness;  k=25 kN/mUnder…

Q: ramophone is driven by a rernor. The mass of each centre of a leaf spring is

A: given:b=5mmt=0.125mmE=210KN/mm2m=20g

Q: The homogeneous rod OA is supported at point 0, and a mass of 2m is attached at the bottom of the…

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Q: A 6-kg uniform cylinder can roll without sliding on a horizontal surface and is attached by a pin at…

A: GivenMass of the cylinder = 6 kgMass of the bar = 4 kgLength of the bar = 12 mm = 0.012 mSpring…

Q: (5) The uniform slender rod (mass m and length L) is pinned to the center of the uniform disk (mass…

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Q: Question 3 A particle of mass m is attached to the midpoint of a taut string of length L and tension…

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Q: Q6. The natural frequency of a spring-mass system is found to be 2 Hz. When an additional massof 1…

A: A spring mass system given if mass m and spring constant k Natural frequency = 2 HzIf mass m+1 and…

Q: 6. A spring with a spring constant of k = 2 is placed in a medium with a damping force numerically…

A: Given data: k=2 lb/ftβ=4 Need to determine the all values of "m" for which the subsequent free…

Q: A close-coiled helical spring undergoes a static deflection of 30 mm when a mass of 2.5 kg is placed…

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Q: A turbine rotor of a ship is of 2000 kg mass and has a radius of gyration of 0.8 m. Its speed is 200…

A: The objective of the question is to determine the maximum couple tending to shear the holding down…

Q: Problem 4: A part of a machine of mass 4.54 kg has a reciprocating motion which is simple harmonic…

A: Given data:To find:The accelerating force and velocity when mass is at 75 mm from mid-stroke.The…

Q: A 220 kg experimental engine is mounted on a test spring mounts at A and B, each with a stiffness of…

A: The mass of the engine is m=220 kg. The stiffness of spring is K=110 kN/m. The radius of gyration is…

Q: A uniform disk of radius r and mass m can roll without slipping on a cylindrical surface and is…

A: Free body diagram of the above setup is shown below,

Q: A ship has a radius of gyration of k=8m, a transverse metacentric height GM of 2m and a displacement…

A: The radius of gyration, kxx = 8 mThe metacentric height, GM = 2 mThe displacement force, F = 156960…

Q: (5) The uniform slender rod (mass m and length L) is pinned to the center of the uniform disk (mass…

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Q: An eccentric plate circular cam of 160 mm diameter and eccentricity 40 mm provides motion to a…

A: Given DataD=160mme=40mmm=2kgk=25N/mmδ1=32mm

Q: A mass of flexible machine part, m, of of 10 Hz. The vibration was caused by the application of a…

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Q: 1. A 20-lb uniform cylinder can roll without sliding on an incline and is attached to a spring AB as…

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Q: A 15-lb uniform cylinder can roll without sliding on an incline and is attached to a spring AB as…

A: Given data: Weight of the cylinder, W = 15 lb. Stiffness of the spring, k = 4.5 lb/in. = 54 lb/ft.…

Q: Two 12-lb uniform disks are attached to the 20-lb rod AB as shown. Knowing that the constant of the…

A: At point A, the system is in the maximum displacement position. So, the system will be at rest. The…

Q: 2. A point mass m is strung on a vertical ring of radius R, and it oscillates freely with respect to…

A: To determine the general movement of the mass m and analyze the resonance phenomenon, let's proceed…

Q: An eccentric plate circular cam of 160 mm diameter and eccentricity 40 mm provides motion to a…

A: Given that, Diameter of cam, D=160 mm Radius of cam, r=D2=1602=80 mm Eccentricity, e=40 mm=0.04 m…

Q: An 800-g rod AB is bolted to a 1.2-kg disk. A spring of constant k = 12 N/m is attached to the…

A: Given Rod AB mass 800 g Mass of the disk = 1.2 kg Spring constant 12 N/m To find Time period of…

Q: For a 15 kg mass, a 300 N/m stiffness spring is used. An initial 60-centimeter displacement is…

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Q: A turbine rotor of a ship is of 2000 kg mass and has a radius of gyration of 0.8 m. Its speed is 200…

A: The objective of the question is to determine the maximum couple tending to shear the holding down…

Q: The 100-lb platform A is attached to springs B and D, each of which has a constant k = 120 lb/ft.…

A: Given: Weight of platform A, wA=100 lb kB=kD=120 lb/ft the newly added weight is 80 lb. first case:…

Q: (5) The uniform slender rod (mass m and length L) is pinned to the center of the uniform disk (mass…

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Q: A body of uniform cross-sectional area A ane density po and at equilibrium displaces a vol…

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Q: A physical pendulum starts moving from a position in which its center of mass is directly above the…

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Q: A spring which stretches by an amount e under a force mi'e is suspended from a support O and has a…

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Q: An 8-kg uniform disk of radius 200 mm is welded to a vertical shaft with a fixed end at B. The disk…

A: Given Data Mass of the uniform disk, M=8 kg Radius of the uniform disk, R=0.2m

Q: n in the Fig. 3, the CM of a cylinder SR is connected to the top of hoop of

A: The mass  if cylinder is .The radius of the cylinder is .The mass of the hoop is .The spring…

Q: (ii) A mass of 5 kg is attached to a spring and rests on a horizontal surface. The mass is then…

A: For spring mass system, Mass (m)= 5 kgTime period (T)= 1.2 secHorizontal displacement =10 mm=0.01 m…

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.