T = Tm sin oft

Q: 7) A counter-rotating eccentric mass exciter is attached to a block, which is supported a…

A:

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: In the case of the forced vibration of a system, determine the range of values of the damping factor…

A: Write the expression for the magnification factor of the vibrating system.

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

A:

Q: A 11-lb block is attached to the lower end of a spring whose upper end is fixed and vibrates with a…

A:

Q: Show that for a small value of the damping factor c/cc , the maximum amplitude of a forced vibration…

A: The amplitude of the forced vibration is given by: When the frequency of the forced vibration…

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

A:

Q: A 3-kg slender rod AB is bolted to a 5-kg uniform disk. A spring of constant 280 N/m is attached to…

A: Given data: The mass of the slender rod is m = 3 kg. The mass of the uniform disk is M = 5 kg. The…

Q: A spring-mass-damper system has a mass of 80 kg suspended from a spring having stiffness of 1000 N/m…

A: As per our guidelines , we are supposed to solve first three sub-parts if multiple sub-parts are…

Q: A 6-kg uniform cylinder is assumed to roll without sliding on a horizontal surface and is attached…

A: Given data Mass of uniform cylinder, Mc = 6 kg. Mass of bar AB, MB = 4 kg. Coefficient of static…

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: The block shown is depressed 1.2 in. from its equilibrium position and released. Knowing that after…

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: air-conditioning chiller unit weighing 2,000 lb is to be supported by four air springs. Determine…

A: Given:W=2000 lbω=7.5 rad/sn=4

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: Q5/ A machine of mass 75 kg are mounted on springs and is fitted with a dashpot to damp out…

A: Answer: (a) The resistance of the dashpot at unit velocity is 423.5 N/(m/s). (b) The ratio of the…

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

A:

Q: A uniform disk of radius r = 120 mm is welded at its center to two elastic rods of equal length with…

A: Given data:  Radius of uniform disk = 120 mm                       Applied couple = 500 mN-m…

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

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Q: A machine weighing 1 kN is to be supported by 3 identical springs (Fig.). what is the stiffness of…

A:

Q: A machine with a mass of “M" is mounted on an elastic foundation, and is found to vibrate m with a…

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Q: A periodic driving force with an amplitude 2N and angular frequency o is applied to a spring-mass…

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Q: A 45-kg motor is bolted to a light horizontal beam that has a static deflection of 6 mm due to the…

A: The mass of the motor is m=45 kg, The static deflection in the beam is δST=6 mm. The mass of the…

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

A:

Q: An object of mass m is supported by a light spring of stiffness k. Show that the solution of the…

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Q: A 180-kg motor is bolted to a light horizontal beam. The unbalance of its rotor is equivalent to a…

A: Given: The mass of the motor,  The unbalance of the rotor,…

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.