Question: 4.22 1. The differential equations for the suspension shown below with input displacement u(t) are 10 100z 10w 100w (a) Assume all initial conditions are

4.22 1. The differential equations for the suspension shown below with

4.22 1. The differential equations for the suspension shown below with input displacement u(t) are 10 100z 10w 100w (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 substitute this expression for W(s) into the 2nd equation, when you solve for Z(s) you get z(s)-b, 40000 330s + 30001 US) 340s2 +300s +3000 (c) What is the transfer function for this system? 92 (d) Consider the following MATLAB command and results >>roots(1 40 300 3000]) ans 33.7442 3.1279 8.8950i 3.1279-8.8950i What are the eigenvalues of this system? (e) What are the time constants of this system? (f) If the input u(t) is a unit step, the general form of the equation for z(t) can be shown to be (g) What is the final value of z(t) and how long will it take to get within 1% of this value? 2. Use the residue theorem to solve the following differential equation for y(t). 22y 44y 88 y(0)5 4. Use separation of variables to solve the differential equation in problem 2. 4.22 1. The differential equations for the suspension shown below with input displacement u(t) are 10 100z 10w 100w (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 substitute this expression for W(s) into the 2nd equation, when you solve for Z(s) you get z(s)-b, 40000 330s + 30001 US) 340s2 +300s +3000 (c) What is the transfer function for this system? 92 (d) Consider the following MATLAB command and results >>roots(1 40 300 3000]) ans 33.7442 3.1279 8.8950i 3.1279-8.8950i What are the eigenvalues of this system? (e) What are the time constants of this system? (f) If the input u(t) is a unit step, the general form of the equation for z(t) can be shown to be (g) What is the final value of z(t) and how long will it take to get within 1% of this value? 2. Use the residue theorem to solve the following differential equation for y(t). 22y 44y 88 y(0)5 4. Use separation of variables to solve the differential equation in problem 2

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Bug-Off Exterminators provides pest control services and sells extermination products manufactured by other companies. Following is the company's unadjusted trial balance as of December 31, 2021....

\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline & \multicolumn{8}{|c|}{ LIST OF AVAILABLE SPRINGS (helical compression springs) } & \\ \hline OD(in) & ID(in) & Length(in) & MaxLoad(lb) & MaxDeflection(in)...

Direction of vehicle's motion e Mass _ J Damper _ 2) Spring Displacement, y Road input, u } il v 2cm A Mass-spring-damper system representative of a vehicle suspension Homework 1: Modeling (ODEs and...

subject: Differential Equations pls read instructions do not use ai. drop all references and link Instructions ODE application. - find an article related to ODE application - provide a short...

Solve below in Wolfram Mathematica a. Prigogine and Lefever described a reaction process that led to oscillations. It is informally referred to as the "Brusselator". The reaction mechanisms are the...

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

^^^^^ solve please Postopening Scenario: Your angel investors are silent in relation to the business; however, they require board meetings. for status updates on the company's nancial health....

Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Chemical Engineering Department MODELING AND SIMULATION OF FCC RISERS A RESEARCH SUBMITTED TO THE...

Part 2: Population growth in a 3-compartment model (25 points) In this we section consider a 3-compartment model. The equations are provided, but you need to solve them, plot the results and consider...

The maker of "Crocs" shoes uses a patented rubber material which is melted and formed into a shoe with an injection molding machine. The rubber is injected into molds in the machine, heated, and then...

1. Assuming a required emergency fund cover of 6 months, what is the client's current emergency fund, taking all her liquid assets into consideration? Balance Sheet Income Statement Assets Income...

Evaluate this statement: It is easier to build an economic model that accurately reflects events that have already occurred than to build an economic model to forecast future events. Do you think...

last two options for the multiple choice are : performance management development A construction equipment manufacturer, Roswell Corporation, is focusing on becoming a leader in sustainability in...

1. Although we share a common border with Canada, its labor relations system is affected by a number of variables that do not greatly affect the United States. Enumerate and explain these variables.

4. Does it make any difference that Mr. Allen is employed in the public sector, instead of the private sector? Give your reasoning. This matter of arbitration stems from an indictment of Thomas Allen...

5. Did the Postal Service act appropriately when it did not grant Mr. Boltons (attorney for Mr. Allen) request for information relevant to Mr. Allens Grievance? If so, explain. If not, explain. This...