1. The differential equations for a suspension system with input displacement (1) are2+102 + 100z 10w + 100ww + 40w = ż+ 10z + 30u(a) Assume all initial conditions are zero and convert the equations above to Laplace domain(b) Demonstrate that if you solve for W(s) in the first equation and then substitutethis expression for W(s) into the 2nd equation, when you solve for Z(s) you getZ(s) =3000+300sLs³ +40s² + 300s + 3000]3(c) What is the transfer function for this system?U(S)

Given the differential equations of suspension system. Required: Laplace domain and transfer…

Answered: 1. The differential equations for a…

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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1. A spring mass system serving as a shock absorber under a car's suspension, supports the M=1000kgmass of the car. For this shock absorber,k=1000N/m and c=2000N s/m. The car drives over a corrugated road with force F=2000sin(wt)N. Use your notes to model the second order differential equation suited to thisapplication. Simplify the equation with the coefficient of x'' as one. Solve x (the general solution) interms of using the complimentary and particular solution method. In determining the coefficients ofyour particular solution, it will be required that you assume w2 -1=w or . Do not 1-w2=-wuse Matlab as its solution will not be identifiable in the solution entry. Do not determine the value of w.You must indicate in your solution:1. The simplified differential equation in terms of the displacement x you will be solving2. The m equation and complimentary solution3. The choice for the particular solution and the actual particular solution xp4. Express the solution x as a piecewise…
Three springs with different spring constants are connected as shown below. You are going to use spring elements to simulate this system. Suppose that the spring constants of the first, second and third elements are k1=3,410 N/m, k2=3,160 N/m and k3=3,380 N/m, respectively. Two horizontal forces are applied to the system (as shown) at nodes. 2 and 3. Find the displacement of node 3 and write your answer in mm (millimetre). Hint: Write your answer with 5 decimal places. For example if you calculated the value 1.2345678, then rounding off to 5 decimal places yields 1.23457 and that is the value you need to type in the answer box. U₁=0 (1) F₂ = 2N U₂ = ? F3 = -1N (2) M U3 = ? (3) U4 = 0
WERK the equivalent spring constant for below if the constant spring is 80 ?N/m k1 m3 k3 k6 m1 k4 m6 m2 k5 840 Non one of them 540 480 O k2
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 ↑
5Find the lengh and divection for (uxv) X(vxu) 179 for the folloning @ u=2i+3j , v= -itj O u=2i-2j +4k,v= -i+j-2k ® u= irj-K, v= o O u= -gi -2j-4k, v= 2i+2j+k O u= i-tj+k, v= i+j+2k
Parameters Mass 5kg A=2 B=7 C(m)=3 D(m)=4.583
Two cables AB and AC are acting on the pole with forces FAB = 540N and FAC = 560N with parameters defining the attachment points shown in the table. We want to write the vector FAB in cartesian vector form. C X Y₂ parameters value units FAB 540 FAC 560 L ZI 3 7₂ 5.5 4 3.5 4 4 Submit Question N N m m m m m FAC A Y₁ Z write the vector FAB in Cartensian Vector Notation. Round your final answers to 3 significant figures. FAB= AB B L X1 N
A spring system is shown here: k₁ 3 Ę k3 2 K₂ www ma 4 Ę₂ Part 1: For this specific system, develop the: a. Global stiffness matrix . b. Boundary condition vector • c. Load vector • d. Reduced system of equations • e. Reaction force equations (i.e., the equations eliminated by the boundary conditions) Part 2: Given: k1 = 70 N/mm, k2 = 110 N/mm, k3 = 165 N/mm, F1 = 150 N, F2 = 100 N, and nodes 1 and 3 are fixed; calculate the: a. Global stiffness matrix b. Displacements of nodes 2 and 4 c. Reaction forces at nodes 1 and 3 d. Spring force in each of the springs
Consider the manipulator provided in the figure. Given the Position vector P w.r.t. to the base frame, derive the Analytical Jacobian for the position. Write your answer as J = [dpx/dq1 dpx/dq2 dpx/dq3; dpy/dq1 dpy/dq2 dpy/dq3; dpz/dq1 dpz/dq2 dpz/dq3] %3D Z3, Z4 Z1, Y, b,s, +b;C;82 -b,c +b3S152 -b;C2 X4 YA #3 b2 b3 O2, 02 P = #2 Z, Y3 #0
*** *Show your correct and complete solution neatly. ASAP! Thanks. Given the vibrating system below: K4 Y(t) =Ysin30t where fc: = 30 and K1 Y=20mm Find the following: m C3 C2 C5 C4 M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2= 40 Ns/m C3= 35Ns/m C4-15 Ns/m C5=10 Ns/m 1. Type of Damping 2. Equation of motion x(t). Assume Initial conditions for displacement and velocity. 3. Graph 2 cycles of the vibrating system. You can use third party app for this.
4. Consider a mass of 500 g placed at the end of a spring with stiffness constant 100 N/m and hanging at rest. The mass is displaced downward by 1.0 cm and released from rest. When the motion sets in, a time-varying force F(t) = cos³ 2t is applied to the spring-mass system. Solve the nonhomogeneous 2nd order differential equation representing the motion. That is, solve for x(t). [Note: Take the downward direction as the negative x-axis.]
The elements of boundary model for box with through hole are OV= 10, E= 15, F= 9, H= 2, G= 1 and C= 1 OV= 10, E= 15, F = 7, H= 2, G= 1 and C= 2 OV= 10, E= 15, F= 9, H= 2, G= 1 and C= 2 OV= 10, E= 15, F= 7, H= 2, G= 1 and C= 1

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