2. An experimental Impulse response of a second order system is shown on the next page. What is the damping ratio , the damped resonant frequency @d and the undamped resonant frequency n of this second order system ?

Q: Ito complete this, it is required to determine the amplitude and phase angle of the transient…

A: Given data as per question stiffness of spring =5000 N/m Mass = 2.5 kg the condition needed for…

Q: An input force f = F:sin(wt) is applied to the body in both systems along the direction x. -Which of…

A: Given : To find : Less steady state amplitude

Q: 1) Laplace equation for this system 2) Solve in time domain for step response 3) Show the step…

A: Solution: Given Data: md2ydt2+bdydt+kyt=ftm=50 kgk = 0.1 N/m   To Find: (a) Laplace equation for the…

Q: A 5 kg object is hung from a spring whose other end is attached to a rigid support. The transient…

A: Solution: Given Data: m=5 kg   To Find: (a) The damping ratio. (b) The stiffness of the spring. (c)…

Q: Consider k₁-1.2, b=7.0, m-1 and initial condition a(0)-0.6 (compatible units). Find the value of k₂…

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Q: For the single degree of freedom system shown below in Figure Q6, and considering only the steady…

A: Given he force input, damping coefficient and forcing frequency.  Required: Amplitude of…

Q: 6. A weight of mass M = 8 kg is suspended by a spring with k = 10 N/ m and c = 1.6 N s/m. Determine…

A: Given , M=8kg    K = 10 N/m    &  c = 1.6 Ns/mthe governing equation of system is,  Mx..+Cx.+Kx…

Q: PROBLEM5: a)Find the natural frequencies and mode shapes of the system shown in Figure 5. b) Find…

A: This is a three degree of freedom system described by variables x1(t) x2(t) and x3(t). x1(0)=1…

Q: For a damped oscillator with a mass of 390 g, a spring constant 66 N/m and a damping coefficient of…

A: mass, m=390 g or 0.39 kgspring constant, k=66 N/mdamping coefficient, c=75 g/s or 0.075 kg/sN=14…

Q: For the single degree of freedom system shown below in Figure Q6, and considering only the steady…

A: In order to solve this problem, we must first determine the natural frequency of the vibration and…

Q: A harmonic force of F(t) = Fo cos(wt) is applied to the system shown in the following figure. With…

A: Response of the displacement: →x(t)=6sin0.4tsin3.7t So the time period for the response:…

Q: . As shown in the spring-damping system, where xt) is the input displacement, x.(1) is the output…

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Q: The mechanical behavior of a biological tissue can be modeled as Maxwell body. The tissue is subject…

A: Write the expression of the force of the tissue,   Ft=F01-e-αt   Calculate the force at t=2 sec,…

Q: . As shown in the spring-damping system, where x() is the input displacement, x.() is the output…

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Q: A Mass, spring, and dashpot system is shown in Figure 2.1. It has a block mass of m = 10 kg The…

A: given data; ⇒f(t)=200cos10t                                                   eq.1⇒ with the help of…

Q: Question 3 (a) A system is critically damped. Derive an expression for the time at which the…

A: Q3(a)The natural frequency of the system, wn = 2.5 rad/sThe initial displacement, Xo = 0 mmThe…

Q: For a critically damping system, the motion will be: harmonic O steady state periodic

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Q: PROBLEM3: Consider the system shown in Figure 3, where m = 70 ton and k = d) Derive the equations of…

A: This is a three degree of freedom system described by variables x1(t) x2(t) and x3(t). Mass of each…

Q: Consider a free response of a underdamped second order system shown below. Given that the…

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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.