ME1014代做、代写 Matlab 程序设计

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ME1014 Dynamic Systems - Lab 1 exercises
This lab is worth 1 mark. This lab exercises must be completed and submitted onto the Blackboard before 20 Mar. at 23:59 hr.
• Make sure that MATLAB had been installed onto your computer. (SCUPI has 2 versions of the MATLAB software: version 2017 and version 2021b. Do not install or use any version newer than 2021b).
• Submit one MATLAB m-file and your workings on paper onto Blackboard. It is the student responsibility to ensure that the MATLAB file can be executed (no marks will be given if the file cannot be executed using MATLAB version 2021b and earlier).
• Late submission will NOT be accepted.
• Warning: any academic misconduct will be reported and zero will be given for the
exercises.
Question 1:
Use Table 2-2 in the textbook to find the Laplace transform of 𝑡 cos(𝜔𝑡) by hand and confirm the result using MATLAB.
Question 2:
Use partial fraction expansion to find the inverse Laplace transform by hand and confirm the result using MATLAB.
4𝑠3 +8𝑠2 +2 𝑠2(4𝑠2 + 1)
Question 3:
Solve the following differential equation by hand with initial conditions 𝑥(0) = 0 and 𝑥̇(0) = 1, and confirm the result using MATLAB “dsolve” command.
2
Question 4:
𝑥̈ + 1 𝑥̇ = 𝑒−2𝑡 4
Apply the final value theorem to determine the steady-state value (if it is applicable) by hand and confirm the result with MATLAB for the following:
𝑋(𝑠) = 𝑠
(4𝑠 + 1)(𝑠2 + 3)
𝑋(𝑠) = 𝑠2 + 3𝑠 + 1 𝑠(𝑠 + 1)2
1