Considering that the displacement motion (x) of the single degree of freedom mass-spring-damper system given in the figure is measured from the static equilibrium position, draw the: a) free body diagram of the system. b) Derive the equation of motion. c) Find its natural frequency.

Q: Question (1). B. The following system is oscillating under the action of a moment M = 20 sin(3r), R…

A: According to the given information we have  d2 which I distance of mass m from the point O…

Q: A disk of radius R = 2 m, whose mass is distributed homogeneously and equals 6 kg, is suspended at…

A: R=2mm=6kgk=0.5 Nm/radl=1mb=Ns/m

Q: The motion of a spring-mass-damper system satisfies the initial value problem: d²x hdx +bu + kx = F,…

A: (d) For poles p±jq, the characteristic equation of the system is, s-p2+q2=0 Here, p and q are…

Q: Figure 2 illustrates a simple mass-damper-spring system. Suppose the output response of the…

A: freebody diagram according to newtons law of motion,ft=f19+fB1+fk1

Q: The mass equals 1 kg, the spring constant equals 25 N/m, and the damping coefficient equals 0.05…

A:

Q: 1. For the system below: a. find the differential equation in terms of 0 (for small values of 0) b.…

A: Given:

Q: D. Figure P1 below shows a block of massm that is attached to two ideal orings and viscous damper.…

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Q: A mass-spring system is driven by the external force S-2, 0 <t < 5 g(t) = 2, 5 <t< 10' 9(t + 10) =…

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Q: The block diagram given below; A) Reduce it B) G1(s)=2/s ; G2(s)=1/4s+2 ; G3(s)=4 ;H(s)=0.5…

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Q: х1 Focos(wt) x2 c2 с1 mtip k2 k1 E

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Q: A rigid bar with mass, M as shown in Figure 1 is pivoted at point 0, and has a point mass m attached…

A: given; k=1200N/mc=60N-s/mM=5kgm=3kgl=1m

Q: -1, -T <t < 0 g(t) = { 1," %3| %3D 0 <t <n•9(t+ 2n) = g(t) [N] s 1 kg, the spring constant equals 25…

A:

Q: k2 m C1 -m

A: given data;

Q: A spring-mass-damper system is at the equilibrium position. The mass m= 10 kg, the damping…

A: Given Data The mass is: The damping coefficient is: The stiffness is: The initial velocity is:…

Q: For the system shown in Figure, find: a) The system equation of motion in terms of θ b) The system…

A: Data given-

Q: Fo sinot

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Q: Find the natural response of the following spring - mass system with m=1, k 1 and the initial…

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Q: A mass attached to a spring is initially (t=0) released 5cm away from the equlibrium position. What…

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Q: 2kg)-spring(100N/m)-damper(c=5) system is left to free damped vibration, the displacement of the…

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Q: COnsider the system

A: For the small angular displacement θ, the inertia force Iα acts in opposite direction, I is moment…

Q: For the problem above: 1. Plot in MATLAB the output-input ratio, |G(iw), and phase lag, 4, as a…

A:

Q: Consider the mass excited by the moving base as shown in the figure. m=3 kg. k=3000 N/m, C=100 kg/s,…

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Q: stem as shown in figure below, M1=m, M2=2m, k1 =5k, k2=10k. 1. Write down the equations of motion…

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Q: A 100-kg tumbler produces a harmonic force of magnitude 5000 N. The stiffness coefficient of the…

A: Givenm=100kgF=5000Nξ=0.2stiffness coefficient k=10×104N/mmaximum deflection ∆max=0.06m

Q: Suppose that the mass in a mass-spring-dashpot system with m=20, c = 19 and k = 3 is set in motion…

A: In mass-spring-dashpot system, the values are Ther initial condition are

Q: A 100-kg tumbler produces a harmonic force of magnitude 5000 N. The stiffness coefficient of the…

A: Given, m = 100 kg F = 5000 N k = 10 x 104 N/m ζ=0.2X = 0.06 m

Q: Mass 15 kg. C=150 Ns/m, k = 200 N/m, a=0.5 m, b=0.75 m Find: 1. Static equilibrium condition 2.…

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

Q: Two identical thin bars, each of mass m and length L, are welded together at a right angle as shown…

A: Solution: Given Data: Displacement, xB=bsinωtStiffness = kLength =L The Equation of Motion of the…

Q: 18. For the single-degree-of-freedom mechanical system shown in the figure: a) determine the…

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Q: Figure 2 shows a roller rolling and slipping at the same time on a slippery surface. The center of…

A: Given:

Q: The mass equals 1 kg, the spring constant equals 25 N/m, and the damping coefficient equals 0.05…

A:

Q: Q4-6 please

A: Given-Data:-JΩ˙ + αΩ = TT = 1000 NmJ = 1600 kg m2α = 200 Ns/rad To-Determine:- 4. Time, t1and t2. 5.…

Q: Question #5 Problem Statement A spring-mass damper system has the following equation of motion * +…

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Q: The equation of motion for a spring-mass-damper system under forced vibration takes the form…

A:

Q: (1) The bar of mass, m= 10kg and length L=lm is fixed at the left end as shown b (a) The equations…

A: Drawing the free body diagram of the system as shown below, Mass of the bar, m=10 kg,Length of the…

Q: Q5:- in the fig M= 20 kg, c=7 N.s/m, k=10 N/M, the excitation is 10 sin5t, find natural frequency,…

A: Given:The mass of the body is The spring constant is .The damping coefficient is .The excitation is…

Q: Question 5. For the mass-spring-dashpot system in Fig.4, where M = 2 kg, K = 8 N/m and f, 3 N-s/m,…

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Q: A mass-spring system is driven by the external force (-2, 0<t< 5 g(t) = 2, 5sts 10' 9(t + 10) = g(t)…

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Q: Problem 4.2 The equation of motion of a certain mass spring damper system is 5X +cX+10 X = f(…

A: The equation is The applied force is

Q: 2. Consider the following compound pendulum, which consists of a thin rod attached to a pivot point…

A: For solution refer below images.

Q: 4) A single degree of freedom (SDOF) system, in which damping is negligible, is initially at rest in…

A: srtep-1

Q: Figure 2 shows a spring-mass system with m= 10 kg, k = k= k3 = ka = 2000 N/m, ks = ko = %3D %3D 3000…

A: Given : To find : Response

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.