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ECMM149 differential equation
创建日期：2024-04-19 16:49:20
所属分类：数学mathematics
标签： ECMM149
differential equation

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ECMM149 Coursework 

 The linear time invariant second order ordinary differential equation governing the behaviour of a damped oscillator is: For the specific values of a, b, c, U and a value of , you can use your student ID last 4 number to define. For example, xxxxx4258, a=4, b=2, c= 4 2 5 40× × = and U=8. In the meantime, the excitation frequency 1ω is a sum of a, b, c and U. (if your ID number has zero, please use 1 to instead of it). Make sure you note the specific values you used in your report. Develop a MATLAB (or Excel) code to estimate the (zero to peak) amplitude, of the displacement x when a ‘steady state’ response i.e. a clear sinusoidal response has been established. Assume zero initial conditions. Separate the 2nd order ODE into a pair of 1st order ODEs and use Euler (or modified Euler) method. You should use a time state that is 1/30 of the period of the oscillation i.e. ℎ = 2 (301)� 1) Using simple Euler method, what is your estimate of and the ratio for 2) Write down the impulse response function IRF for the system and create a vector of values the same length as the vector of input values u(t) you created for 1). 3) Use the MATLAB ‘conv’ function using the IRF and u vectors from 2) to provide an alternative estimate. 4) Use a larger time step ℎ = 2 (51)� and comment on the effect. 5) Sticking to the correct time step, repeat the numerical solution for nine extra values of i.e. and tabulate values of H. 6) Plot H for ignoring any of such strange values. 7) Now construct the frequency response function H directly using the method from lecture 6 and a result from the tutorial, 8) Plot values of this H for and overlay on the result for 6) above. 9) Use the MATLAB ‘diff’ function or your solution to a numerical calculus tutorial question to differentiate your time series from your calculations for 1) above to obtain velocity (differentiate once) and acceleration (differentiate again). Plot the velocity from the first differentiation and compare that with the values obtained directly from the numerical solution of the ODE. Comment on the comparison.

Report: Create a report where you show the differential equation governing the damped oscillator with your specific parameters (from your student ID number). Then, answer to each of the questions describing your solution and including any figures where asked. Include your Matlab code in your report. See next page for marking scheme: This could be a time-consuming exercise, so it is recommended to devote your major efforts to 1) 3) and 7) which attract most marks, marking scheme is as follows:
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 25 5 15 10 5 5 15 5 15
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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