A B

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

A:

Q: A mass-spring-damper system, with constants m=6.5 kg, c=12N*s/m y k=6.5 N/m, It is released from…

A:

Q: The period of vibration of the system shown is observed to be 0.6 s. After cylinder B has been…

A: Given T1 = 0.6 s T2 = 0.5 s MB = 3lb To find The weight of cylinder A The constant of the spring

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

A: Given Mass of the cylinder = 6 kg Mass of the bar = 4 kg Length of the bar = 12 mm = 0.012 m Spring…

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: A 64-lb block is attached to a spring with a constant of k = 1 kip/ft and can move without friction…

A: Given Data: The weight of the block is: w= 64 lb. The value of the spring constant is: k=1 kip/ft.…

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: A collar with mass m that slides on a frictionless horizontal rod is attached to a spring with…

A: The static deflection of the spring is The natural frequency of the system is The amplitude of the…

Q: The free-fixed rod ( length of 2 m, diameter of 0.5 mm, density of 300 kg/m') vibrates in lengthwise…

A:

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 vibrometer used to measure the amplitude of vibrations consists essentially of a box containing a…

A: For the steady-state motion of the system, the solution can be given as,

Q: Determine a natural frequency of vibration as a function of k₁, k₂. g and W of a spring-mass system…

A:

Q: (a) Interpret the phenomena occurred that explained by the mechanical engineer. (b) If the flexible…

A: For solution refer below images.

Q: n electric motor with a mass of 260 kg and a rotating nbalance, is mounted near the end of a steel…

A:

Q: A body of mass of 50 kg is supported by an elastic structure of stiffness 10 kN/m. The motion of the…

A: The natural frequency of vibration can be calculated using the formula:ω=kmwhere k is the stiffness…

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

A:

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: In the system shown,m= 2 kg, k= 1000 N/m, theta= 30 degrees and the friction coefficient between the…

A: Draw the free body diagram.

Q: 2. A element was made of a material with the material parameters of a b MPa, os 600MPa, o-1-360MPa,…

A: Given:To find:

Q: A bungee jumper weighing 160 lb ties one end of an elastic rope with a length of 200 ft and…

A: Natural frequency formula ω =km weight  = 160 lb stiffness k = 10 lb/in

Q: The 6-kg uniform rod AC is attached to springs of constant k = 500 N/m at B and k = 620 N/m at C,…

A:

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: A mass of flexible machine part, m1 of 10 ×1 kg was observed to vibrate badly at frequency of 10 Hz.…

A:

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

A: Let's displaced the point 'A' by a small displacement 'x' which makes a small angle 'θ' at point…

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

A: A system consists both potential energy U and kinetic energy K,  according to law of conservation of…

Q: A 7-kg block is suspended by three identical springs, each with k = 200 N/m. The bottom of the block…

A:

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

A:

Q: A mass of flexible machine part, m, of 10 × 1 kg was observed to vibrate badly at frequency of 10…

A:

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

A:

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: k A k 30 ст С 1 W 60 cm

A: given; weight =Wmass(m)=weight(W)gBC=60cm=0.6mAB=30cm=0.3m

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…

Q: A 4-kg collar can slide on a frictionless horizontal rod and is attached to a spring with a constant…

A: Given data: The mass of the collar, m = 4 kg. The spring constant, k = 450 N/m. The periodic…

Q: The period of oscillation of the system shown in Fig. a is observed to be 0.5 s. After the spring of…

A:

Q: A mass of flexible machine part, m, of 10 x 2 kg was observed to vibrate badly at frequency of 10…

A:

Q: (a) Interpret the phenomena occurred that explained by the mechanical engineer. If the flexible…

A: For solution refer below images.

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.