A single degree of freedom system consists of a mass of 20 kg and a spring of stiffness 4000 N/m. The amplitudes of successive cycles are found to be 50, 45, 40, 35, ...mm. Determine the nature and magnitude of the damping force and the frequency of the damped vibration.

Q: A spring with a stiffness of 300 N/m is connected to a 15 kg mass. A displacement of 60 cm to the…

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Q: Accordingly, determine the mass and stiffness values in the initial system.

A: Given: T=0.35 s T'= time period increase by 10% =1.1T m' increase by 2 lb =0.907 kg To determine:…

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…

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A: first of all making free body diagram of the given system , Now, according to newton law, sum of…

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A: The static deflection of the spring is The natural frequency of the system is The amplitude of the…

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

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Q: T1= 0.62 s T2= 0.54 s K1= 2440 n/m

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Q: = what will be the percentage

A: Given data; mass(m)=2kgharmonic exciting…

Q: A 15 kg block hangs from a spring with a spring constant of 12 kN/m.  The block is initially held so…

A: Given data: Mass of the object (m) = 15 kg Spring constant (k) = 12 kN/m Need to determine the…

Q: Determine the natural frequency of free oscillations for the pulley system if the stiffness of the…

A: Ans Given Now draw the FBD of the pulley asNow take equilibrium in vertical direction as Now force…

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Q: A rotating mass machine has a mass of 200 kg and It rests on four shock absorbers, one of which has…

A: Approach: The resulting amplitude can be find out using the formula for the magnification factor…

Q: Determine the frequency of the free vibrations, when a body of mass 20 kg is suspended from a spring…

A: The solution is given as follows

Q: A mass of flexible machine part, m, of of 10 Hz. The vibration was caused by the application of a…

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Q: A metal block, placed on a rough surface, is attached to a spring and is given an initial…

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Q: Q2) ) A mass of 1 kg is to be supported on a spring having a stiffness of 9800 N/m. The damping…

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Q: 4.3. In a single degree of freedom undamped spring-mass system, the mass m = 3 kg, and the stiffness…

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Q: 1.4 mm 1.3mm 1.5 0.5 -0.5 -1 -1.5 6. 8 10 12 14 16 18 Displacement, x (mm) 2.

A: In under-damped system, the amplitude of the vibration also changes with time. This variation can be…

Q: A system consists of a mass, a spring, and a dashpot. The mass weighs 19.3 lb. The spring constant…

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Q: A mass of 21.5 kg is vibrating freely at the end of 3 springs connected in parallel. The spring…

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Q: A set of scales consists of an instrumented spring from which the mass of the measured object can be…

A: Initial mass, mi=10 kgFinal mass, mf=10+20=30 kg

Q: A mass of flexible machine part, m, of 30 kg was observed to vibrate badly at frequency of 10 Hz.…

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Q: An oscillator system without damping has a natural frequency of omega 0 = pi rad/s.  Several types…

A: Given : ω0 = 3.14 rad/s ζ=0.1,0.5,1 To find: a) Frequency of oscillator b) Displacement at t = 2…

Q: A mass of 0.10 kg is attached to a spring. It is pulled 200 mm to the right of its position when the…

A: Given: Mass→m=0.10 Kg Initial amplitude→X1=200 mm=0.2 m Shifting of the mass after each swing=30…

Q: A mass of flexible machine part, m1 of 10 ×1 kg was observed to vibrate badly at frequency of 10 Hz.…

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Q: A simplified vibration measuring instrument is used to measure the vertical acceleration of…

A: Given : ω=10 r/s m=1.2 kg k=104 N/m To find : a) max acceleration b) amplitude of duct

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A: Given that: mass of piston (unbalanced mass) m = 10.6 kg mass of engine M = 447.8 kg Stroke length =…

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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 2-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal…

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Q: A machine of mass 112.7 kg is mounted on four parallel springs each of stiffness 3.2 x 105 N/m. When…

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Q: n object of mass 2 kg is attached to a spring of stiffness 200 N / m on a horizontal frictionless…

A: Frequency is given by,ω=kmω=2002ω=10 radian/s

Q: one complete cycle. The period of oscillation is observed to be [7] s. Find the spring constant k…

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Q: A 1-kg block attached to an Ideal massless spring and fixed on the other end on a horizontal…

A: Spring force  : The Spring force is the force exerted by a compressed or stretched spring upon any…

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Q: A weight attached to a 525N/m spring is a damped system. When the weight is displaced and left free,…

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Q: • A helical spring has a stiffness of 1 N/mm. What mass should be hung on it, so that it may…

A: Given: Spring stiffness k=1N/mm or 1000N/mMass (m)=?Time period (T)=1.5seconds

Q: A block of mass m hangs from a spring with a spring constant k. The block is initially held so that…

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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.