vibrations - solve and show sollution Obtain the mathematical model relating to the displacement x, (t) and x; (t) for thespring-mass-damper system shown in the figure.What would be the effect of neglecting the mass?X(1)KmSpringDamperX(1)

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Answered: Obtain the mathematical model relating…

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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Find the motion of the system in the figure below with mass 0.25 kg, no damping, spring constant 1 kg/sec², and driving force 120 cos(0.5t) - 56 sin(1.5t) nt, assuming zero initial displacement and velocity. For what frequency of the driving force would you get resonance? y(t) = = m Spring Mass Dashpot Mass-spring system Resonance for the frequency:
Whats the first equation (circled) and how did we get it ?
The motion of a spring-mass-damper system satisfies the initial value problem: d²x m- +bd + kx = F, x(0) = 0; *(0) =1 di? dt Given m = 1 kg, b= 5 Ns/m, k = 4 N/m, and F = 5 N. (a). What is the natural frequency of the system? (b). Is this system under damping or critical damping or over damping? Explain it. (c). Solve the given initial value problem. (d). The location of poles of X(s) affects the behavior of the system. How to choose parameters b/m and k/m so that the poles are placed at - 4+4j?
Please find the question attached.
Please solve (c) and (d)
3. Suppose the model of a vehicle suspension is given below. Write the equation of motion in matrix form (not in State Space form). Calculate the natural frequencies for k₁ k2 10 N/m, m2 = 50kg, and m₁ = 2000kg. -= - - 103 N/m, 1 x1(c) m1 www m1 Car mass k₁ Car spring k1 k₂ Tire stiffness www x2(1) m2 Tire mass м2 k₂ ↑
Hello, please solve this problem. Thank you very much
Sub- Mechanical vibrations
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
pls answer question a and b sir pls use this matrix num sir (ad 200153) subject (vibration)
Answer completely.
i, Consider the following 1-DOF system, where k :0-3 kg, calculate the natural frequency in rad/s and Hz. Also find the period of scillations and the maximum displacement if the spring isinitially displaced 10 am with no initial velocity. 857.8 N/m and m = 49.2 x

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Obtain the mathematical model relating to the displacement x, (t) and x; (t) for the spring-mass-damper system shown in the figure. What would be the effect of neglecting the mass? X(1) K m Spring Damper X(1)