0.6 -0.41 s 0.5 VO 0.4 0.5 in. 0.3 0.2 0.12 in. 0.1 -0.1 0.2 0. 0.6 0.8 Time (s) -0.2 -0.3 (1) (2) Displacement (in.)

Q: 3) A one-degree-of-freedom system has an effective mass M=4-kg, an effective spring stiffness…

A:

Q: 3) A one-degree-of-freedom system has an effective mass M-4-kg, an effective spring stiffness…

A: To find  (a) The natural frequency ωn and critical damping ratio ζ (b) The response q as a function…

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

A:

Q: The mass of a single degree damped vibrating system is 7.5 kg and makes 24 free oscillations in 14…

A:

Q: 8) If the mass of a simple pendulum m and its length L are doubled, then the period of time will be…

A:

Q: 1)A 10 kg body suspended from the end of a vertical spring of negligible mass stretches it 10 cm.…

A: Free body diagram of spring

Q: Problem 2. A counterrotating eccentric mass exciter as shown below is used to determine the…

A:

Q: A machine supported symmetrically on four springs has a mass of 160 kg. The mass of the…

A:

Q: The barrel of a field gun weighs 1500 lb and is returned into firing position after recoil by a…

A: Understand that the system will return to its original position without oscillation when the system…

Q: Consider a mass-and-spring system containing two masses m, = 1 and m2 = 1 whose displacement…

A:

Q: A machine of mass 30 kg is placed on an elastic foundation. A sinusoidal force of magnitude 28 N is…

A: The system is modeled as a mass attached to a spring in parallel with a viscous damper with a…

Q: A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A:

Q: A 16.3 kg motor is bolted to a light horizontal beam which has a static deflection of 0.19 cm due to…

A: GIVEN DATA UNBALANCE MASS m=0.02 kg Eccentricity e=15.8cm SPEED N=900rpm We have to calculate…

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 spring with a spring constant of 1200lbf/ft is attached to block with a mass of 96.6lbm…

A:

Q: the constant of the support spring (without damping) which only transmits only up to 28% of the…

A: Drawing the figure for the given as shown below –

Q: A sensitive electronic system, of mass 25 kg, is supported by a spring-damper isolator that rests on…

A: We have to solve problems

Q: 6) The system, shown below, hangs in the vertical plane. The bar and the sphere have equal masses…

A: Given- Mass of bar = mass of sphere = (m) = 2 kg, Natural frequency fn=2 Hz ωn=2πfn=2π×2= 12.57 rads…

Q: A simplified model of a washing machine is shown. A bundle of wet clothes forms a weight wb of 20 lb…

A:

Q: Q1: A machine of mass 25 kg is placed on an elastic foundation. A sinusoidal force of magnitude 25N…

A: according to the given information we have a system modeled as a mass that is attached to the spring…

Q: A mass weighing 5 lb stretches a spring 9 in. If the mass is pushed upward, contracting the spring a…

A:

Q: When a 40-kg machine is placed on an elastic foundation, its free vibrations appear to decay…

A:

Q: Problem 2. A projectile of mass m= 10 kg travelling with a velocity of 50m/s strikes and becomes…

A: In the above question we have to find the damping coefficient and maximum displacement and the…

Q: frequency given that W =1N, L0 =0.1m, b=0.15 m, and k = 80 N/m

A: Solution : Given data : W =1N,                  the free length L0 =0.1m,                  length 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: Q.4 A device to produce vibrations consists of the two counter-rotating wheels, each carrying an…

A: Given:-            Relation of force transmitted by neglecting the damping. We get,…

Q: Question. In a car crash test, a car travelling at a constant speed of 60 km/h collides into a…

A: Given: Mass of the car→m=2150 Kg Spring constant→K=80.98 N/mm Damping constant→C=21.19 N/mm Initial…

Q: A 64-lb weight suspended from a spring (spring constant is 200 lb/ft) is released from rest 0.4 ft…

A:

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 mass weighing 4 lbs. stretches a spring 1.5 inches. The mass is given a positive displacement of 2…

A: Solution: Given Data: W=4 lbsx=1.5 inδ=2 inu=0F=2 cos 3t

Q: A machine of mass 25 kg is placed on an elastic foundation. A sinusoidal force of magnitude 25 N is…

A: Given: Mass of the machine is m=25 kg, sinusoidal force is F0=25 N  amplitude is Xmax=1.3 mm and…

Q: A spring of stiffness 2 kN/m is suspended vertically and two equal masses of 4 kg each are attached…

A: Given: K , stiffness=2000N/m mass  ,m=4kg           find  1. Amplitude of vibration         2.…

Q: A helical spring, of negligible mass, and which is found to extend 0.25 mm under a mass of 1.5 kg,…

A: Given :        m = 60 kg       r = 12.5 mm = 0.0125 m         x = 5 mm = 0.005 m

Q: Two blocks A and B, each of mass m , are supported as shown by three springs of the same constant k…

A:

Q: n order to reduce vibrations being transmitted to the floor, a machine of mass m = 150kg is…

A:

Q: For the spring-mass-damper system shown to the right, x is measured from the static equi- librium…

A:

Q: A 30 kg object is undergoing lightly damped harmonic oscillations. If the maximum displacement of…

A:

Q: 13. The maximum permissible recoil distance of a gun is specified as 0.5 m. If the initial recoil…

A:

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

A: Write the expression of the motion. mx¨+bx˙+kx=0

Q: A 2-kg block is supported by a spring with a constant of k= 128 N/m and a dashpot with a coefficient…

A: Calculate the natural frequency of the block. Here,  is spring constant of the spring, and  is mass…

Q: A weight of 50 N stretches a spring 0.25 m. The weight is drawn down 0.05 m below its equilibrium…

A: Given Data⇒ data for first spring : Weight (W1)=50 N stretch in spring (x)=0.25 m Weight is drawn…

Q: A massless bar of length 1 m is pivoted at one end and subjected to a force F at the other end. Two…

A: Where: M - Moment about point O I   - Moment of inertia about point O α - Angular acceleration of…

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.