set of initial conditions for the system of Prob. 6.20 such that free vibrations occur only at the system's lowest natural frequ

Q: Two uniform rods AB  and CD, each of length l and mass m, are attached to gears as shown. Knowing…

A: Write the expression of the gear ratio between the two gears.

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: 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 simple pendulum consisting of a bob attached to a cord of length l = 800 mm oscillates in a…

A: (i) the frequency of oscillation is given by        = 3.502 rad/s         = 0.557 Hz

Q: Problem 2 A railroad car of masse 20000 kg travelling at a velocity v=10 m/s is stopped at the end…

A:

Q: Two small weights w are attached at A and B to the rim of a uniform disk of radius r and weight W.…

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: Two small spheres, A and C, each have a mass m and are attached to rod AB that is supported by a pin…

A: Consider the rod AB is deviated through an angle θ. Draw the free body diagram of the system.…

Q: A 360-lb motor is supported by springs of total constant 12.5 kips/ft. The unbalance of the rotor is…

A: Write the given data:

Q: Q6/ Find the natural frequency of vibration for the system shown, when K1 = 10 N/mm, K2 = 5 N/mm, K3…

A:

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: 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: 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: A small collar of mass 1 kg is rigidly attached to a 3-kg uniform rod of length L = 750 mm.…

A: FBD of pendulam is shown in figure.

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 50-kg block is supported by the spring arrangement shown. The block is moved vertically downward…

A: Given: The mass of the block, m = 50 kg The amplitude of the motion, x = 60 mm = 0.06 m The…

Q: A motor weighing 350 lb is supported by four springs, each having stant of 750 lb/in. The unbalance…

A: a)   The resonant frequency is equal to the natural frequency of the system. Given, weight of the…

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: An inverted pendulum consisting of a rigid bar ABC of length l and mass m is supported by a pin and…

A: Given Data: The spring constant is k. The length of the rod is l. The distance of the spring from…

Q: Denoting by δst the static deflection of a beam under a given load, show that the frequency of…

A: Given: Static deflection of the beam is δst and mass of the beam is neglected. Stiffness of the beam…

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: A 14-oz sphere A and a 10-oz sphere C are attached to the ends of a 20-oz rod AC are attached to the…

A: Given mass of sphere 'A', mA=14 oz=14×0.0625 lb=0.875 lb; ⇒Weight, WA=0.875 (lb)×g…

Q: Two uniform rods Ab and Cd is length l and mass m, are attached to gears as shown. Knowing that the…

A: Distance of A = Distance of C 2rθA=rθc2θA=θcDiff w.r.t to time2θ.A=θ.c

Q: 1. The block m is suspended from three springs with stiffness k, and k, as shown. The frequency of…

A:

Q: A uniform rod AB can rotate in a vertical plane about a horizontal axis at C located at a distance c…

A: Initial K.E = 0 Initial P.E = mgh=mgc(1-cosθm) 1-cosθm=2sin2θm2=θm22 Initial P.E =mgcθm22

Q: A torsional pendulum has a centroidal mass moment of inertia of 0.3kg.m2 and when given an initial…

A: The initial twist given to the shaft is . The torsional force acting on the shaft is . Here, the…

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.