YEDITEPE UNIVERSITY

MECHANICAL ENGINEERING DEPARTMENT

ME 372 COMPUTER AIDED MECHANICAL ENGINEERING

ASSIGNMENT I

ALPER ERAL

280705037

I. INTRODUCTION

At the laboratory hour of ME 372 the task given was to investigate some

characteristics of a single degree-of-freedom system. While doing the

investigation, concepts such as Euler’s method, finding the exact solution and

taking derivatives were used. In order to solve the problem in a modular and

flexible way, operations, which were dealing with ordinary differential equations

and initial value problems, stated in the report were made. Throughout the report

detailed information about the process will be given via diagrams and MATLAB

codes.

II. RESULTS AND DISCUSSION

Functions exact.m and derive.m given during the laboratory hour were

changed into the forms stated below. function [yexact] = exact(t, y0)

m=0.6297;c=0.05;I=0.7176E-2;g=9.81;lg=0.8446E-2;

T=c/(2*I*wn);wn=sqrt((m*g*lg)/I);w=wn*sqrt(1-(T^2));c1=y0(1);c2=-(T*wn*c1)/w;

yexact=exp(-T*wn*t))*(c1*cos(w*t)+c2*sin(w*t);

end

function f = deriv(tk, yk)c=0.01;lg=0.8446E-2m=0.6297;I=0.7176E-2;c=0.01;g=9.81;

f = [yk(2);(-c/I)*yk(2)-((m*g*lg)/I)*yk(1)];

After changing some parts of the function lab1_main.m, following diagrams

were drawn via MATLAB. In order to understand the affects of the c and h

variables, different values for them were used.

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Figure 2: Diagram drawn when h=0.05

Figure 3: Diagram drawn when h=0.1

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Figure 4: Diagram drawn when h=0.2

Figure 5: Diagram drawn when h=0.1 and c=0

Figure 6: Diagram drawn when h=0.1 and c=0.005

Figure 7: Diagram drawn when h=0.1 and c=0.02

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Figure 8: Diagram drawn when h=0.1 and c=0.05

Throughout the trials, it can be commented that changes in c cause changes

approximate function and the changes in h affects the exact function. When

observed, it can be recognized that, using greater values for c and h have negative

effects on performance of the methods such as lack of accuracy and stability.

When c= 0.005 and h=0.1, the results are in harmony. They match accurately. The

optimum values for c can be considered between 0.005 and 0.05 and for h between

0.05 and 0.1.

III. CONCLUSION

After conducting numerous trials, it can be concluded great values for c and h

makes the function unstable and not accurate. While choosing the values for that

kind of an operation, this fact should be taken into account. One of the finest

results were observed for c= 0.005 and h=0.1. To have optimum results, h can be

taken between 0.05 and 0.1 and c between 0.005 and 0.05.

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