iven an oscillat

Q: 1. Consider two pendulums, 1 and 2, with the same string length L, but with different bob masses m1…

A: As per our guidelines we are supposed to answering only one question. Kindly repost other questions…

Q: 5.) Consider the spring-mass-damper system with damping constant c, spring constant k, and external…

A: As per company policy, we are restricted to solve three sub-part of one question at a time. Please…

Q: minimum damping coefficient such that there is no oscillation

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Q: Problem 1 An object of mass m = 0.2 kg is hung from a spring whose spring constant is 80 Nm-1. The…

A: Given, m=0.2kg. k=80N/m, Restoring force  Resistive force  1) Differential equation of the motion is…

Q: A mass, m of 22kg consider one vertical motion only with angular displacement, 0 = wt, with spring…

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Q: A mass of 1.42 Kg is connected to a spring of spring constant 8.71 N/m. An oscillation is started by…

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Q: needs complete detailing. take N=70 b=20 a) The figure shows an oscillatory system where the mass…

A: Given, M=100kgk=5N/mm=20kgs=70N/m

Q: Two mass placed on top of each other have a mass of 20 g each and there is a coefficient of static…

A: At the position of amplitude the restoring spring force will be F=kAand therefore the acceleration…

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 vibrating system has the following parameters: m = 18 kg, K = 70 N / cm, c = 0.8 N.s / cm.…

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Q: The period ra of damped linear oscillation for a certain 0.7 kg mass is 0.25 s. If the stiffness of…

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Q: A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: How is constant amplitude sustained in forced oscillations?

A: When the oscillation is carried out by external force then this is known as forced oscillation.

Q: 6. A body weighing 16 lb is suspended by a spring in a fluid whose resistance in Ib wt. is twice the…

A: Given: The body weight, m = 16 lb The fluid resistance, R = 2(dy/dt) The pull, P = 25 lb The stretch…

Q: Consider a damped mass-spring system with mass 3 kg, spring constant 10 N /m, and damping…

A: Given; The mass of system, m = 3 kg The spring constant, k = 10 N/m The damping coefficient, c = 5…

Q: The logarithmic decrement of damping of a tuning fork oscillating with a frequency 1,1 Hz is 5.…

A: Given: δ=5 ω=1.1 Hz To find: Time interval for amplitude to decrease by 7.1 times

Q: A mercury thermometer having a time constant of 0.1 min is placed in a temperature bath at 100 F and…

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Q: 5. A mass hangs from a helical spring. The periodic time of free vibration in a vertical direction…

A: Given data: The relation of the time period of the cycle with angular frequency can be shown as,

Q: For small positive damping, c, in the sinusoidally forced mass-spring system mz" + cz' + kr = Ggcos…

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Q: A machine having a mass of 5 kg vibrates in a viscous medium. A harmonic force of 50 N acting on it…

A: Given, m=5 kgF=50 NResonant xmax=20 mm=0.02 mtp=0.3 s

Q: 1. A damped single degree of freedom has a mass of 1100 kg and spring stiffness of 500,000 N/m. If…

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Q: determine magnification factor of forced vibration produced by oscillator fixed at middle of the…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A machine is represented as a single degree of freedom spring-mass-damper system. The machine has a…

A: The mass of the machine is m = (100+01) kg = 101 kgThe out-of-balance mass is mb = 0.125 kgThe…

Q: A weight of 50 N is suspended from a spring of stiffness 4000 N/m and is subjected to a harmonic…

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Q: A disk of massm and radius R rolls without slip while restrained by a dashpot with coefficient of…

A: Drawing the free body diagram of the disk as shown below, IC=12mR2  ...... 1∑Fx=mx¨ Taking moment…

Q: s suspended by a spring of stifness of 30KN/m and a dashpot of damping constant 1000 N.s/m.…

A: Given: m = 100 KKg k = 80 KN/m c= 1000 N-εm F0 = 80 N w = 6 πradsec mx ¨+ cx˙ + kx = F0 sin wt----…

Q: The logarithmic decrement of damping of a tuning fork oscillating with a frequency 1,1 Hz is 5.…

A: Given, Frequency of oscillations = f = 1.1 Hz Logarithmic decrement = δ = 5   Let us say after t…

Q: A machine, weighing 3000 N, is supported on a resilient foundation. The static deflection ofthe…

A: (a)Consider W as the weight force, k as the stiffness of the foundation, and ds as the deflection.…

Q: 6. Consider the following 1-DOF system, where k = 857.8 N/m and m = 49.2 * :0-3 kg, calculate the…

A: Natural frequency of an object is defined as the frequency at which the object begins to vibrate in…

Q: The maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/sec, and the…

A: Note: Since you have posted a question with multiple sub-parts, we will solve first three sub- parts…

Q: A machine of mass 500kg is mounted through four mounting pads that exhibit linear elasticity and…

A: Given data: The mass of the machine, m = 500 kg. The distance moved by the pad, x = 10 mm. The…

Q: of spring-mass-coulomb damping, with mas of 0.1kg, stiffness of 10N s/m and a damping force of 0.1N…

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Q: The logarithmic decrement of damping of a tuning fork oscillating with a frequency 1,1 Hz is 5.…

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Q: A heavy machine, weighing 3000 N, is supported on a resilient foundation. The static deflection of…

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Q: The maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, and the period…

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Q: Given a SDOF of spring-mass-coulomb damping, with mass of 0.1kg, stiffness of 10N.s/m and a damping…

A: The value 10 N.s/m must be damping coefficient since N.s/m is the unit of damping coefficient.

Q: Q2\ The period of damped linear oscillation for a certain 1 kg mass is o.32 sec. If the stiffness of…

A: Mass = 1 kg time period = 0.32 second Stiffness = 850 N/m

Q: A 96lb weight stretches a spring 3.2ft in equilibrium. it is attached to a dashspot with damping…

A: Given : W = 96 lb x = 3.2 ft c = 18 lb-sec/ft x0 = 15 inches = 1.25 ft v0 = 12 ft/sec To find:…

Q: A mass weight 100 N is supported by a spring of stiffness 20 KN/m and a viscous damper. During free…

A: Given Data F=100 N K=20 kN/m

Q: Mechanical Vibration Lesson A 65 kg industrial sewing machine has an imbalance value of 0.15 kgm in…

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Q: (a) The position of a mass in a spring-mass system is given as x(t) = 2cos4t. Find the period of…

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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.