ww. ww- CO A B

Q: (iii) The drum described in part 1b (i) is driven by a belt attached to a motor. Figure (i) shows…

A: 1 Given,F1=force on tight side of beltF2=force on slack side of beltμ=coefficient of…

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: 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: 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: 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: A connecting rod supported by a knife-edge at point A. For si oscillations the angular acceleration…

A: To given thatα=-6θω at θ=22.4°          =22.4×π180rad is zerofor ωmax:dωdt=0…

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: The weightless rod carries two masses m, one at a distance L from the pivot o the other at 2L. If…

A:

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: 4.21. Assuming small angular oscillations, derive the differential equation of motion of the system…

A: given; ⇒lenth of rod =l⇒mass of rod =m⇒weight of rod(w)=mg

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

A:

Q: The simple pendulum shown oscillates in the vertical plane (the plane of the figure) as the pendulum…

A:

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: (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 homogeneous wire of length 2l is bent as shown and allowed to oscillate about a frictionless pin…

A: Given data: The length of the wire is 2l. The period of oscillation when the angle β = 0 is ? = ?0 .…

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: work due to spring (N.m) O a. -5.57 о ь.-6.68 O C.-4.45 O d.-7.79 O e.-2.23 angular velocity in…

A:

Q: A slider crank mechanism, FIG. A5, consists of a piston of 2.5 kg mass and a crank of 50 mm…

A:

Q: Two uniform rods, each of weight W = 24 lb and length L = 2 ft, are welded together to form the…

A: Given Data: W=24 lbL=2 ftk=3 lb/in   To Find: Determine the frequency of the resulting motion.

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: 3.26. It was observed that the damped free oscillations of a single degree of freedom system is such…

A: Given Data X12=0.48X6

Q: A connecting rod is supported by a knife-edge at point A; the period of its small oscillations is…

A: Equation of motion.  -mgsinθ=(mrα)r+mk2αα+grr2+k2sinθ=0 For small oscillations,            sinθ=θ…

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: 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: work due to spring (N.m)  angular velocity in position (2) (rad/s)

A: For solution refer below images.

Q: A 20 kg motor is bolted to a light horizontal beam which has a static deflection of 0.2 cm due to…

A: Option d is correct.

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 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: 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 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 40 kg motor is bolted to a light horizontal beam which has a static deflection of 0.2 cm due to…

A: GIVEN DATA UNBALANCE MASS m=0.02kg eccentricity e=16cm SPEED N=2400rpm   WE HAVE TO CALCULATE…

Q: The work done by spring is  The work done by weight is  Polar moment of inertia about B is…

A: Given that, Initial position, CD2=CB2+BD2CD=1202+3502CD=370 mm, ∆x1=370-150∆x1=220 mm, Final…

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: 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: Denoting by dst the static deflection of a beam under a given load W, show that the frequency (Hz)…

A: Answer: The correct answer is option (b).

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…

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.