Question laFor the spring/mass system below, determine the natural frequencies if:m₁= 9kg, m2=1kg, k₁=24N/m, k2=3N/m and k3=16 N/m.[Ans: 1.7 and 4.4 rad/s]wwwvyuk₁M₁00000M2*********00000k₂

To determine the natural frequencies of the system, we need to calculate the effective spring…

Answered: Question 1a For the spring/mass system…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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For the system shown in Figure 2, u (t) and y (t) denote the absolute displacements of Building A and Building B, respectively. The two buildings are connected using a linear viscous damper with damping coefficient c. Due to construction activity, the floor mass of Building B was estimated that vibrates with harmonic displacement that is described by the following function: y(t) = y,cos (wt). k/2 Building A H k/2 M(t) C 73(1) Building B Equivalent (Building A) 00000000 Figure 2: Single-degree-of-freedom system in Problem 2. 111 uft) Please compute the following related to Building A: (a) Derive the equation of motion of the mass m. (b) Find the expression of the amplitude of the steady-state displacement of the mass m. (1) (Building B)
A 2 DOF mass-spring system shown below with n = 1, k = 8, and m initial conditions 2₁ (0) = 1, 2₂(0) = 0, ₁ (0) = 0, and ₂(0) = 1. (a) Find the natural frequencies and normalized modal matrix [X] for the system. T x₁ (1) (b) Using modal analysis and the Cartesian solution form, find the free vibration re- sponse of the system x₁(t) and x2(t). Ţ x2₂ (1) www. 00000 = m m₁ = 00000 k₁ = k 00000 k₂ = nk m₂ = m k3= k = 2 DOF mass-spring system. 2 with the
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2.- Determine if the system shown (modulator) is: (1 point) 2.1- Linear 2.2. Invariant in time.
The quarter-car model of a vehicle suspension and its free body diagram are shown in Figure 1. In this simpliﬁed model, the masses of the wheel, tire, and axle are neglected, and the mass m represents one-fourth of the vehicle mass. The spring constant k models the elasticity of both the tire and the suspension spring. The damping constant c models the shock absorber. The equilibrium position of m when y=0 is x=0. The road surface displacement y(t) can be derived from the road surface profile and the car’s speed. Draw free body diagram (FBD) and derive the equation of motion of m with y(t) as the input, and obtain the transfer function. If assume: m=300 kg k=20000, 40000, 60000 N/m c=1000, 3000, 5000 N.s/m Plot magnification ratio vs frequency ratio (r=0-4) diagrams for the parameters given above (you can draw the three curves in one diagram for three different k values and do the same for the three c values as well). Use the derived transfer function to model the system and plot…
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Q2: For mass-spring system shown. The mass is given an initial displacement x(0)= 0.1 m, and released from rest. Find: 1- The position of the mass after 2 seconds. 2- The velocity of the mass after 2 seconds. 3- Plot the response for three cycles and label the result from 1 & 2. 4- What is the period of oscillation? 5- What is the acceleration of mass (m) after 5 second? Į x(t) k=100 N/m m = 4 kg
Hello, please solve this problem. Thank you very much
ll b) Obtain the mathematical model of the system shown in Figure Q2b using Newton's second law of motion, F=ma. k₁ w 3- 777777 C1 7771 k₂ D 7777 Figure: Q2b Page 2 of 7 A C2 1112
Ex. A vehicle wheel, tire and suspension assembly can be modeled crudely as a single degree of freedom spring mass system. The mass of the assembly is measured to be about 300kg. its frequency of oscillation is observed to be π rad/sec. What is the approximate stiffness of the tire, wheel and suspension assembly? ilippines) Accessibility: Investigate

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Question 1a For the spring/mass system below, determine the natural frequencies if: m₁= 9kg, m2=1kg, k₁=24N/m, k2=3N/m and k3=16 N/m. [Ans: 1.7 and 4.4 rad/s] m₁ 00000 m₂ 00000 k₁ k₂ k3