Lab. 1 - Example 2Modeling of the system with 2 masses dealt with in Lect. 4

Correct directions of the forces in FBDDevelopment History: see inside of this folded "cell"

0. Setting notebook styles - optional (read inside of the cell)

1. Preparing Mathematica

2. Defining the problem (see also Lecture 4 for details)

3. Defining basic equations

eq1 = -m1 y1££@tD + k Hy2@tD - y1@tDL ã 0;

eq2 = -m2 y2££@tD - k Hy2@tD - y1@tDL ã 0;

4. Defining initial conditions - SI units

ic1 = y1@0D ã 0.5;

ic2 = y1£@0D ã -0.2;

File: lab_1_demo_2.nb Date: 2/25/11 14:01:56

ENME 599, Instructor: S. Spiewak, sspiewak@ucalgary.ca , ph. (403) 220 8976 Page 1

ic3 = y2@0D ã 0;

ic4 = y2£@0D ã 0;

5. Solving

m1 = 10; m2 = 20; k = 100;

res = NDSolve@8eq1, eq2, ic1, ic2, ic3, ic4<, 8y1@tD, y2@tD<, 8t, 0, 5<D;

The above cell solves the ODE(s) and returns the result, res, which may be confusing. In particular, this solution has many properties of a symbolic function although it is obtained by numerical method. Some explanation(s) will be given in class/lab

Expressingthesolutionascontinuousfunctionsoftime

ysoln1@t_D = y1@tD ê. resP1T;

ysoln2@t_D = y2@tD ê. resP1T;

In the above cell the solution is converted into an explicit function of time. This function is tested and plotted below

6. Plotting : y1[t] - red ; y2[t] - blue

Plot@8ysoln1@tD, ysoln2@tD<, 8t, 0, 5<, PlotRange Ø All,PlotStyle -> 88Red, Thickness@0.005D<, 8Blue, Thickness@0.005D<<D

1 2 3 4 5

-0.4

-0.2

0.2

0.4

Cool Plot

imageWidth = 700;

File: lab_1_demo_2.nb Date: 2/25/11 14:01:58

ENME 599, Instructor: S. Spiewak, sspiewak@ucalgary.ca , ph. (403) 220 8976 Page 2

shapePlot = Plot@8ysoln1@tD, ysoln2@tD<, 8t, 0, 5<, PlotRange Ø All,PlotStyle Ø 88Red, Thickness@0.005D<, 8Blue, Thickness@0.005D<<,Frame -> True, FrameLabel Ø 8"Time, @sD", "Response, @mD"<,FrameStyle Ø Directive@Black, 36D, FrameTicksStyle Ø Directive@Blue, 28D,TextStyle Ø 8FontFamily Ø "Helvetica", FontWeight -> "Bold", FontSize Ø 16<,ImageSize -> 8imageWidth, imageWidth ê GoldenRatio<,GridLines -> Automatic, GridLinesStyle Ø Directive@Gray, DashedDD

0 1 2 3 4 5-0.4

-0.2

0.0

0.2

0.4

Time, @sD

Response,@mD

File: lab_1_demo_2.nb Date: 2/25/11 14:01:58

ENME 599, Instructor: S. Spiewak, sspiewak@ucalgary.ca , ph. (403) 220 8976 Page 3