A mass spring system with two masses and three springs is described by the linked first...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A mass spring system with two masses and three springs is described by the linked first order ODEs in Equations (2.1) and (2.2), x; and x2 represent the displacement from equilibrium of each respective mass, and t represents time. dx - M +(K + K)x Kx = 0 dt M +(K + K3)x - Kx = 0 dx dt Equation (2.1) M: has a mass of 1 kg, M a mass of 2 kg, K: a spring constant of 1 kg s, K a spring constant of 2 kg s and K3 a spring constant of 2 kg s. (a) Equation (2.2) Substitute the given values into the coupled ODEs in Equations (2.1) and (2.2). (4 Marks) (b) Take the Laplace transform of Equation (2.1), given x:= -1, x2 = 2, and dx=dx2=0 at t = 0. (6 Marks) dt dt (c) Take the Laplace transform of Equation (2.2), given x; = -1, X2 = 2, and dx=dx=0 at t = 0. (6 Marks) dt dt X (s) = (d) Taking your answers for part b) and part c), show that solving for X gives the equation shown in equation (2.3). (6 Marks) 2s + 5s (s + 4)(s + 1) Equation (2.3) (e) Resolve equation (2.3) into partial fractions. (6 Marks) A mass spring system with two masses and three springs is described by the linked first order ODEs in Equations (2.1) and (2.2), x; and x2 represent the displacement from equilibrium of each respective mass, and t represents time. dx - M +(K + K)x Kx = 0 dt M +(K + K3)x - Kx = 0 dx dt Equation (2.1) M: has a mass of 1 kg, M a mass of 2 kg, K: a spring constant of 1 kg s, K a spring constant of 2 kg s and K3 a spring constant of 2 kg s. (a) Equation (2.2) Substitute the given values into the coupled ODEs in Equations (2.1) and (2.2). (4 Marks) (b) Take the Laplace transform of Equation (2.1), given x:= -1, x2 = 2, and dx=dx2=0 at t = 0. (6 Marks) dt dt (c) Take the Laplace transform of Equation (2.2), given x; = -1, X2 = 2, and dx=dx=0 at t = 0. (6 Marks) dt dt X (s) = (d) Taking your answers for part b) and part c), show that solving for X gives the equation shown in equation (2.3). (6 Marks) 2s + 5s (s + 4)(s + 1) Equation (2.3) (e) Resolve equation (2.3) into partial fractions. (6 Marks)
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
In this problem, we consider the analysis of the combined information from both raters on the shoulder flexion (SF) scores in the posture measurement study. Thus, the questions below concern the data...
-
Find the point-slope form of the line pass- ing through the given points. Use the first point as (x 1 , y 1 ). (-3,4), (2,5)
-
Shannon AG, changed from the average-cost to the FIFO cost flow assumption in 2019. The increase in the prior year's income before taxes is 1,200,000. The tax rate is 40%. Prepare Shannon's 2019...
-
For each section illustrated, find the second moment of area, the location of the neutral axis, and the distances from the neutral axis to the top and bottom surfaces. Consider that the section is...
-
Rework Problem 10.14, part a, but exclude the region information. a. Comment on the difference in the models you have found. Is there indication that the region information substantially improves the...
-
Doublewide Dealers has an ROA of 10%, a 2% profit margin, and an ROE of 15%. What is its total assets turnover? What is its equity multiplier?
-
Q3: Lessons 8, 9 [CLR 3, 4, 5, 7] (15 marks) a) The bookstore owner in Q2 wants to know if taking 10 observations of his worker inserting disks into the used textbooks were sufficient. He would be...
-
Which of the following is a false statement about Health Savings Accounts (HSAs)? a. Taxpayers who contribute to an HSA must carry qualifying high-deductible health insurance. b. HSAs are available...
-
The course project is designed to incorporate several different themes or learning objectives from the course into a comprehensive analysis that is designed to measure how well you understand the...
-
Pick one of the companies on the Dow Jones Industrial Average (DJIA) and look up their financial information on Google. Look at their financial information and tell us any interesting trends that you...
-
Tobin's Barbeque has a bank loan at 10% interest and an after-tax cost of debt of 6%. What will the after-tax cost of debt be when the loan is due if a new loan is taken out yielding 12%. Note: Do...
-
Why does the U.S. Treasury sell securities? please describe the auction process. What is the difference between competitive bid and noncompetitive bid? The market of Treasury bills is extremely...
-
The Venezuelan bolivar versus the US dollar is 7 to 1, i.e., 7 bolivars buy one dollar. The ER between the Swiss franc and the US dollar is one Swiss franc to 1.1 US $. Finally, the bolivar trades...
-
Question 5 Tries remaining: 1 Marked out of 0.17 Constructing Financial Statements from Account Data Barth Company reports the following year-end account balances at December 31, 2011. Prepare the...
-
Amazon.com, Inc.'s financial statements are presented in Appendix D. Financial statements of Wal-Mart Stores, Inc. are presented in Appendix E. Instructions for accessing and using the complete...
-
An auto-parts manufacturer is considering establishing an engineering computing center. This center will be equipped with three engineering workstations each of which would cost $25,000 and have a...
-
Figure 29.21 shows the decay series for plutonium-239. Use the information in the figure to (a) Determine the two different decay schemes by which the isotope of radon associated with this chain can...
-
Can all of the kinetic energy be lost in the collision of two objects? Explain.
-
In a mass spectrometer, a doubly charged ion having a particular velocity is selected by using a magnetic field of 100 mT perpendicular to an electric field of 1.0 kV/m. This same magnetic field is...
-
A golf ball is hit from the tee and travels above level ground. Accounting for air resistance, where is the horizontal location of the peak of the flight: at a position that is less than half the...
-
The velocity of an object is given in SI units by \(\vec{v}=\left(a t-b t^{2} ight) \hat{\imath}+c \hat{\jmath}\), with \(a=14 \mathrm{~m} / \mathrm{s}^{2}, b=10 \mathrm{~m} / \mathrm{s}^{3}\), and...
-
A cannon fires a shell at an angle such that the shell's initial velocity has a horizontal component of \(20 \mathrm{~m} / \mathrm{s}\) and a vertical component of \(35 \mathrm{~m} / \mathrm{s}\)....
Study smarter with the SolutionInn App