F At = -(2.4 N•s)k 180 mm D 150,mm B 150'mm 180 mm

Q: 125 mm B The blade of an oscillating fan and the rotor of its motor shown have a total weight of 1…

A: Given Data Mass, m=1Kg The radius of gyration, K=0.100m Width of the fan, b=0.125m N1=2000 rpm

Q: A slender 12.7-kg rod can rotate in a vertical plane about a pivot at A. A spring of constant k= 89…

A: Calculated kinetic energy at position (1). Mass movement of inertia about hinge and work due to…

Q: Two disks each have a mass of 5 kg and a radius of 300 mm. They spin as shown at the rate of w1 =…

A: Given Mass of disk = 5 kg Radius of disk = 300 mm Rotation of spin = 1200 rpm Reaction CD = 350 N To…

Q: The blade of a portable saw and the rotor of its motor have a total weight of 2.5 lb and a combined…

A: Given data: Rotation of blade,  w1 = 1500 rpm Total weight, W = 2.5 lb. Radius of gyration, kz = 1.5…

Q: 5) A slender 5-kg rod can rotate in a vertical plane about a pivot at B. A spring of constant k =…

A: Given:-             slender mass = 5 kg               spring stiffness = 5000 N/m…

Q: The gear train shown consists of four gears of the same thickness and of the same material; two…

A: Calculate the mass of the disk of radius r. Here, ρ is the density of the material, V is the volume…

Q: Two uniform rods AB and CE, each of weight 20 N and length 1 m, are welded to each other at their…

A: The mass moment of inertia of an object is defined as mass times the length of the square of…

Q: Two uniform cylinders, each of mass m = 6 kg and radius r = 125 mm, are connected by a belt as…

A: Given data: The mass of the cylinders is m=6 kg. The radius of the cylinder is r=125 mm. The angular…

Q: The 7.5-kg rod BC connects a disk centered at A to crank CD. Knowing that the disk is made to rotate…

A: to find: a = ? Cy = ? N

Q: A rope is wrapped around a cylinder of radius r and mass as shown. Knowing that the cylinder is…

A: moment of inertia of cylinder about its axis of rotation (I) = mr2/2

Q: A driver starts his car with the door on the passenger’s side wide open ( _ θ = 0). The 100-lb door…

A: Given data: The mass of the door is; m = 100 lb. The centroidal radius of gyration of the door is; k…

Q: The ABC bar has a mass of 2.4 kg and is connected to a support on B. An 800 g D sphere reaches the…

A: Given data: Mass of rod ABC is m = 2.4 kg. Mass of sphere is M = 800 g. Velocity of ball is v1 = 3…

Q: A slender 9 lb rod can rotate in a vertical plane about a pivot at B. A spring of constant k=30…

A:

Q: Question 3 The gear rack has a mass of 6 kg, and the gears each have a mass of 4 kg and a radius of…

A: Given: mass of the rack→mr=6 Kg mass of each gear→mg=4Kg Radius of gyration of each gear→k=30…

Q: The steel roll shown has a mass of 1230 kg, a centroidal radius of gyration of 150 mm, and is lifted…

A:

Q: Two uniform rods AB and CE, each of weight 3 lb and length 2 ft, are welded to each other at their…

A: Given data Weight of the rods AB and CE W = 3lb Length of the rod AB and CE = 2ft Angular velocity…

Q: A 48-kg advertising panel of length 2a = 2.4 m and width 2b = 1.6 m is kept rotating at a constant…

A: Given Draw side view of panel with principal axes Write Moment of inertial about x’ and y’

Q: Disks A and B are made of the same material, are of the same thickness, and can rotate freely about…

A: Given data Mass of disk A, mA = 8 kg. Radius of disk A, rA = 150 mm. Radius of disk B, rB = 100 mm.…

Q: L A collar with a mass of 2 kg is rigidly attached at a distance d = 300 mm from d the end of a…

A:

Q: The 10-oz disk shown spins at the rate w1 = 750 rpm, while axle AB rotates as shown with an angular…

A: The angular velocity vector is: Let the origin be at C with the centroidal axis x, y, and z.

Q: The double pulley shown has a mass of 3 kg and a radius of gyration of 100 mm. Knowing that when the…

A: Given   rA=0.080 m(Smaller pulley)rA'=0.15 m(Bigger pulley)k=0.1 m(Radius of gyration)Now taking…

Q: A thin rectangular plate of weight 15 lb rotates about its vertical diagonal AB with an angular…

A: h=92+122=15        Moments of inertia:                Ix=1121532.2912=0.0218 slug…

Q: The flywheel of a steam engine has a radius of gyration of 1 m and mass 1S00 kg. The starting torque…

A:

Q: A slender 9-lb rod can rotate in a vertical plane about a pivot at B. A spring of constant k = 30…

A: Write the given data: W= 9 lbk=30 lb/ftLs=6 inLrod=24 in=2 ft12 in1 ft

Q: 2. Arm ACB rotates about point C with an angular velocity of 40 rad/s counterclockwise. Two friction…

A:

Q: 18.2 A thin rectangular plate of weight 15 lb rotates about its vertical diagonal AB with an angular…

A:

Q: Each of the gears A and B has a mass of 675 g and a radius of gyration of 40 mm, while gear C has a…

A: Given data: Mass of gears A & B = 675 g                    Radius of gyration of gears A & B…

Q: A small 2-kg sphere B is attached to the bar AB of negligible mass that is supported at A by a pin…

A: Consider the diagrams shown below for the system for the small angular displacement. Here, the…

Q: A 6-lb homogeneous disk of radius 3 in. spins as shown at the constant rate w1 = 60 rad/s. The disk…

A: Given: The mass of the disc, m = 6 lb The radius of the disc, r = 3 in The speed of the disc, w1 =…

Q: A 1200-kg satellite designed to study the sun has an angular velocity of w0 = (0.050 rad/s)i +…

A: Calculate the values of principal moment of inertia along the x, y and z-axis,

Q: 5. AS-kg uniform disk is attached to the 3-kg uniform rod BC by means of a frictionless pin AB. An…

A:

Q: The blade of an oscillating fan and the rotor of its motor have a total mass of 300 g and a combined…

A: ω1=ω1iω1=2π(1800)60=188.5 rad/sω=ω1i+ω2jHG=Ixω1i+Iyω2j Thre reference frame rotating with Ω=ω2j…

Q: A uniform rod AB of mass m = 6.4kg is welded at its midpoint G to a vertical Shaft GD. Knowing that…

A:

Q: 125 mm | B The blade of an oscillating fan and the rotor of its motor shown have a total weight of 1…

A:

Q: A bar of mass m = 5 kg is held as shown between four disks each of mass m’ = 2 kg and radius r = 75…

A: Given: The mass of bar, m = 5 kg The mass of each disk, m' = 2 kg The radius of the disk, r = 75 mm…

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.