A body weighing 16 lb is suspended by a spring in a fluid whose resistance in lb.ωt. is twice the speed of the body in ft/sec. A pull of 25 lb. ωt would stretch the spring 3 inches. The body is drawn 3 inches below equilibrium position in the fluid and then released find the period of oscillations and the time required for the damping factor to be reduced to one-tenth of its initial value. SOLVE USING DIFFERENTIAL EQUATIONS

Q: A mass of one kg stretches a spring 49 cm in equilibrium. It is attached to a dashpot that supplies…

A: From the solution refer below images.

Q: 1- Two mass-spring-damper systems A & B. System A has = 0.1 and wn = 20 rad/sec, and system B has =…

A: Here we will apply the damping coefficient comparison

Q: A 160 pound object is suspended from a spring with spring coeficient 3 Ibt. The whole system is…

A: Given: F(t) = -32sin(2t)+21cos(2t) m= 160 lb k = 3 lb/ft c= 1 lb sec/ft

Q: The frequency of a damped harmonic oscillator is one-half the frequency of the same oscillator with…

A: Natural frequency: The number of vibrations executed by a body when it is vibrating freely in one…

Q: A mass of m kg is on a spring with spring constant 10 N/m and dampingconstant 3 Ns/m. Find the mass…

A: solution given data: K =10 NmC=3 N-sm

Q: A mass of 2 slugs is attached to a spring whose constant is 8 lb/ft. The medium offers a damping…

A: Given data: The mass of the object attached to the spring is m = 2 slugs. The spring constant is s…

Q: A mass weighing 4 pounds is attached to a spring whose constant is 2 lb/ft. The medium offers a…

A:

Q: A mass of 3kg stretches a spring from its naturał length of 8.3°cm; to a length of 13,2cm.The mass…

A:

Q: The nat. period of an undamped system is 3 s, but with a damping force that is proportional to the…

A:

Q: A mass m = 4 kg is attached to both a spring with spring constant k = 197 N/m and a dash-pot with…

A: Mass of the system (m): 4 kgSpring constant (k): 197 N/mDamping coefficient (c): 4 N·s/mInitial…

Q: The 4-kg cylinder is attached to a viscous damper and to the spring of stiffness k-800 N/m. Write…

A: Given data:- Mass of the block =4 kg spring of stiffness = 800 N/m. c=124 N.s/m c=80 N.s/m To…

Q: A mass weighing 16 pounds stretches a spring 83 feet. The mass is initially released from rest from…

A:

Q: A spring with an m-kg mass and a damping constant 3 (kg/s) can be held stretched 2.5 meters beyond…

A: The damping constant is The stretched in spring by a  force is .

Q: Consider the following system (m 27 kg and k=3kN/m). in k Suppose that the damping coefficient is…

A: Given , morning =27kg and K = 3000 N/m  C = 0.5 *C_c

Q: • Compute the solution to +2x+2x=0 for the initial conditions x0 = x (0) = 0 mm, vo = (0) = 1 mm/s…

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Q: 2) Consider the compound pendulum-spring-mass system below where the mass mr is added to the tip and…

A: To findFind the equation of motion and natural frequency.Givenmass of pendulum = stiffness of spring…

Q: 2- Two mass-spring syst the mass of system B answer with a plot

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Q: Find the damping coefficient c for this system.

A: Given: m= 24 kg k= 3000 N/m no of cycles (N)=5 xNx0=110x: Amplitude To find: Damping coefficient c…

Q: This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both…

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Q: 3) Consider the simple pendulum-spring-mass system below, where mass m is added to the tip of the…

A:

Q: You have a prototype Slinky with a lump of coal at the end. This forms a damped spring-mass system.…

A: Here Given:- m=1 k=3 b=1

Q: A spring with a mass of 1 kg has a spring constant 43 kg/s2. If the spring begins at equilibrium…

A:

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.