Matlab Assignment 01 (from The Book “matlab An Introduction With Applications” 4 Edition )

Matlab Assignment 01 (From the book “Matlab an Introduction with Applications” 4th edition Amos Gilat Department of Mechanical Engineering the Ohio State University) Submitted by: Muhammad Irfan Malik (2017-CH-52) Submitted to: Dr. Kashif Date of submission: October 25, 2019.

Chapter 01: Q13 (a): >> x=12; >> z=tand(4*x) z= 1.110612514829193 >> y=(4*tand(x)-4*tand(x)^3)/(1-6*tand(x)^2+tand(x)^4) y= 1.110612514829193 As z=y (Hence given Identity proved)

Q13 (b): >> x=12 x= 12 >> y=sind(12)^3 y= 0.008987455040201

>> z=(1/4)*(3*sind(x)-sind(3*x)) z= 0.008987455040201 As y=z (Hence given Identity proved)

Q14: >> a=(5*pi)/8; >> b=(pi/8); >> x=sin(a)*cos(b) x= 0.853553390593274 >> y=(1/2)*(sin(a-b)+sin(a+b)) y= 0.853553390593274 As x=y (Hence given Identity proved)

Chapter 02: Q11: >> i=[1 6 -3 -3 -3 -3 -3 -3 -3] i= 1

6

-3 -3

-3

-3 -3

-3 -3

-3 -3

-3 -3

>> f=i(3:9) f= -3 -3 -3

Here “f” is a row vector contains 7 elements that are all (-3).

Q24 (a): >> a=[7 2 -3 1 0]

a= 7

2

-3

1

0

>> b=[-3 10 0 7 -2] b= -3 10

0

7 -2

>> c=[1 0 4 -6 5] c= 1

0

4

-6

>> u=ones(3) u= 1 1 1

1 1 1

1 1 1

>> u(1,:)=a(1:3) u= 7 1 1

2 1 1

-3 1 1

2 1 1

-3 1 1

>> u u= 7 1 1

>> u(2,:)=b(1:3) u= 7 2 -3 -3 10 0

5

1

1

1

>> u(3,:)=c(1:3) u= 7 -3 1

2 -3 10 0 0 4

Q24 (b): >> a=[7 2 -3 1 0] a= 7

2

-3

1

0

>> b=[-3 10 0 7 -2] b= -3 10

0

7 -2

>> c=[1 0 4 -6 5] c= 1 0 4 -6 >> v=zeros(3) v= 0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

>> v v= 0 0 0 >>

5

>> v(:,1)=a(3:5) v= -3 0 0 1 0 0 0 0 0 >> v(:,2)=b(3:5) v= -3 0 0 1 7 0 0 -2 0 >> v(:,3)=c(3:5) v= -3 0 4 1 7 -6 0 -2 5

Chapter 03: Q12(a): >> v=[2 4 6 8 10] v= 2

4

6

8 10

>> s=[1 1 1 1 1] s= 1 1 1 >> a=v.\s

1

1

a= 0.500000000000000 0.250000000000000 0.166666666666667 0.125000000000000 0.100000000000000

Q12 (b):

>> v=[2 4 6 8 10] v= 2

4

6

8 10

>> q=[1 1 1 1 1] q= 1 1 1 >> b=v.^2.\q

1

1

b= 0.250000000000000 0.062500000000000 0.027777777777778 0.015625000000000 0.010000000000000

Q12 (c): v= 2 4 6 >> c=v./2

8 10

c= 1

2

3

4

5

Q12 (d): >> v=[2 4 6 8 10] v= 2 4 6 >> d=v./v

8 10

d= 1

1

1

1

1

Q34:

i1

i3

i2

i4 V1 =12V V2 =24V R1=20Ω R2=12Ω R3=8Ω R4=6Ω R5=10Ω

Using Mesh Analysis



For Loope1 V1 –(i1- i3)R1 – (i1 – i2)R2 = 0 V1- i1R1+ i3R1- i1R2+i2R2=0 12-20i+20i3-12i1 +12i2 =0 12-32i1+12i2+20i3+0i4 =0 (Equ1)



For Loope2 -V2 – (i2- i4)R4 – (i2- i1)R2 =0 -V2 - i2R4 + i4R4 - i2R2 +i1 R2=0 -24-6i2 +6i4 -12i2 +12i1 =0 -24+12i1-18i2+0i3+6i4= 0 (Equ2) For Loope3 V2 –(i3-–i1)R1–i3R3 =0 V2 - i3R1+ i1R1- i3R3=0 24-20i3+20i1-8i3=0 24+20i1+0i2-28i3+0i4 =0 (Equ3)





For Loope4 - (i4 -i2) R4 - - i4R5 =0 - i4R4 + i2R4 – i4R5 =0 -6i4+6i2-10i4 =0 0+0i1+6i2+0i3-16i4 =0 (Equ4) Summary of Equations: 12-32i1+12i2+20i3+0i4 =0 -32i1+12i2+20i3+0i4 = -12 (Equ1) -24+12i1-18i2+0i3+6i4= 0 12i1-18i2+0i3+6i4 = 24 (Equ2) 24+20i1+0i2-28i3+0i4 =0 20i1+0i2-28i3+0i4 = -24 (Equ3) 0+0i1+6i2+0i3-16i4 =0 0i1+6i2+0i3-16i4 =0 (Equ4) Now from Matlab >> A=[-32 12 20 0; 12 -18 0 6; 20 0 -28 0; 0 6 0 -16] A= -32 12 20 0 12 -18 0 6 20 0 -28 0 0 6 0 -16

B= -12 0 -24 0 >> inv(A)

ans = -0.116666666666667 -0.088888888888889 -0.083333333333333 -0.033333333333333 -0.088888888888889 -0.131216931216931 -0.063492063492063 -0.049206349206349 -0.083333333333333 -0.063492063492063 -0.095238095238095 -0.023809523809524 -0.033333333333333 -0.049206349206349 -0.023809523809524 -0.080952380952381 >> X=inv(A)*B X= 3.400000000000000 2.590476190476190 3.285714285714286 0.971428571428571 Therefore i1= 3.4 A i2= 2.59 A i3= 3.28 A i4= 0.97 A

Chapter5: Q3(a): >> x=[0:3] x= 0 1 2 3 >> y=(x+1).*(x-2).*(2.*x-0.25)-exp(x) y= -0.500000000000000 -6.218281828459046 -7.389056098930650 2.914463076812332 >> plot(x,y,'g')

Q3(b): >> x=[-3:6] x= -3 -2 -1

0

1

2

3

4

5

6

>> y=(x+1).*(x-2).*(2.*x-0.25)-exp(x) y= Columns 1 through 6 -62.549787068367863 -17.135335283236614 -0.367879441171442 -0.500000000000000 6.218281828459046 -7.389056098930650 Columns 7 through 10 2.914463076812332 22.901849966855764 27.086840897423400 -74.428793492735110 >> plot(x,y)

Q4: >> x=[-2:2] x= -2 -1

0

1

2

>> y=sqrt(abs(cosd(3.*x)))+sin(x).^2 y= 1.824078996602090 1.707387950717973 1.000000000000000 1.707387950717973 1.824078996602090 >> plot(x,y,'r')

Q8(a): >> t=[-30:-1.6] t= Columns 1 through 20 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -14 -13 12 -11 Columns 21 through 29 -10

-9 -8

-7

-6 -5

-4

-3 -2

>> x=(3.*t)./(1+t.^3) x= Columns 1 through 6 0.003333456794696 0.003567328194194 0.003826704933716 0.004115435423229 0.004438122332859 0.004800307219662 Columns 7 through 12 0.005208710120813 0.005671543646227 0.006198929275852 0.006803455723542 0.007500937617202 0.008311461067367

Columns 13 through 18 0.009260847196021 0.010382736156352 0.011721611721612 0.013337285121517 0.015311702515494 0.017759562841530 Columns 19 through 24 0.020845396641575 0.024812030075188 0.030030030030030 0.037087912087912 0.046966731898239 0.061403508771930 Columns 25 through 29 0.083720930232558 0.120967741935484 0.190476190476190 0.346153846153846 0.857142857142857 >> y=(3.*t.^2)./(1+t.^3) y= Columns 1 through 6 -0.100003703840883 -0.103452517631622 -0.107147738144048 -0.111116756427192 0.115391180654339 -0.120007680491551 Columns 7 through 12 -0.125009042899515 -0.130445503863225 -0.136376444068752 -0.142872570194384 0.150018752344043 -0.157917760279965 Columns 13 through 18 -0.166695249528383 -0.176506514657980 -0.187545787545788 -0.200059276822762 0.214363835216916 -0.230874316939891 Columns 19 through 24 -0.250144759698900 -0.272932330827068 -0.300300300300300 -0.333791208791209 0.375733855185910 -0.429824561403509 Columns 25 through 29 -0.502325581395349 -0.604838709677419 -0.761904761904762 -1.038461538461539 1.714285714285714

Q8(b): >> t=[-0.6:40] t= Columns 1 through 6 -0.600000000000000 0.400000000000000 1.400000000000000 2.400000000000000 3.400000000000000 4.400000000000000 Columns 7 through 12 5.400000000000000 6.400000000000000 7.400000000000000 8.400000000000000 9.400000000000000 10.400000000000000 Columns 13 through 18 11.400000000000000 12.400000000000000 13.400000000000000 14.400000000000000 15.400000000000000 16.399999999999999 Columns 19 through 24

17.399999999999999 18.399999999999999 19.399999999999999 20.399999999999999 21.399999999999999 22.399999999999999 Columns 25 through 30 23.399999999999999 24.399999999999999 25.399999999999999 26.399999999999999 27.399999999999999 28.399999999999999 Columns 31 through 36 29.399999999999999 30.399999999999999 31.399999999999999 32.399999999999999 33.399999999999999 34.399999999999999 Columns 37 through 41 35.399999999999999 36.399999999999999 37.399999999999999 38.399999999999999 39.399999999999999 >> x=(3.*t)./(1+t.^3) x= Columns 1 through 6 -2.295918367346939 1.127819548872181 1.121794871794872 0.485698866702644 0.253076617705439 0.153160679476469 Columns 7 through 12 0.102231421647819 0.072963852491412 0.054649651423845 0.042445393664183 0.033911186362412 0.027712050478566 Columns 13 through 18 0.023068455303856 0.019500698250808 0.016700566323682 0.014462749047199 0.012646225402818 0.011151546801138 Columns 19 through 24 0.009906958100779 0.008859636395386 0.007969999934268 0.007207916836657 0.006550122105703 0.005978422166281 Columns 25 through 30 0.005478424061863 0.005038621168927 0.004649725556356 0.004304173787756 0.003995756526013 0.003719337727390

Columns 31 through 36 0.003470639491691 0.003246075594267 0.003042621507187 0.002857712047526 0.002689160140399 0.002535091861707 Columns 37 through 41 0.002393894136321 0.002264172350458 0.002144715787310 0.002034469278313 0.001932509824736 >> y=(3.*t.^2)./(1+t.^3) y= Columns 1 through 6 1.377551020408163 0.451127819548872 1.570512820512821 1.165677280086347 0.860460500198491 0.673906989696463 Columns 7 through 12 0.552049676898223 0.466968655945034 0.404407420536453 0.356541306779136 0.318765151806673 0.288205324977084 Columns 13 through 18 0.262980390463959 0.241808658310023 0.223787588737337 0.208263586279672 0.194751871203395 0.182885367538663 Columns 19 through 24 0.172381070953558 0.163017309675108 0.154617998724800 0.147041503467809 0.140172613062045 0.133916656524701 Columns 25 through 30 0.128195123047590 0.122942356521821 0.118103029131446 0.113630187996746 0.109483728812768 0.105629191457886 Columns 31 through 36 0.102036801055704 0.098680698065709 0.095538315325665 0.092589870339842 0.089817948689322 0.087207160042707 Columns 37 through 41

0.084743852425759 0.082415873556673 0.080212370445404 0.078123620287219 0.076140887094601 >> plot(x,t,':b',y,t,'-g')

Chapter4: Q2: >> r=4.85/100; P=100000; y=10:30; M=(P*(r/12))./(1-(1+(r/12)).^(-12.*y)); tbl=[y,M]; disp(M) disp(y) disp(tbl) 1.0e+03 * Columns 1 through 6 1.053338409158346 0.979037203037794 0.917383650308490 0.865457759352513 0.821173725417141 0.783001870280961

Columns 7 through 12 0.749794854663779 0.720675227539015 0.694960459103126 0.672111647628188 0.651697614333117 0.633369256928701 Columns 13 through 18 0.616840897707781 0.601876497400946 0.588279315611263 0.575884052781169 0.564550805582168 0.554160365576284 Columns 19 through 21 0.544610525327117 0.535813148778964 0.527691827570959 Columns 1 through 20 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Column 21 30 1.0e+03 * Columns 1 through 6 0.010000000000000 0.011000000000000 0.012000000000000 0.013000000000000 0.014000000000000 0.015000000000000 Columns 7 through 12 0.016000000000000 0.017000000000000 0.018000000000000 0.019000000000000 0.020000000000000 0.021000000000000 Columns 13 through 18 0.022000000000000 0.023000000000000 0.024000000000000 0.025000000000000 0.026000000000000 0.027000000000000 Columns 19 through 24 0.028000000000000 0.029000000000000 0.030000000000000 1.053338409158346 0.979037203037794 0.917383650308490 Columns 25 through 30

0.865457759352513 0.821173725417141 0.783001870280961 0.749794854663779 0.720675227539015 0.694960459103126 Columns 31 through 36 0.672111647628188 0.651697614333117 0.633369256928701 0.616840897707781 0.601876497400946 0.588279315611263 Columns 37 through 42 0.575884052781169 0.564550805582168 0.554160365576284 0.544610525327117 0.535813148778964 0.527691827570959 Note: Here is the link of book from which assignment was completed https://ecedmans.files.wordpress.com/2014/03/matlab-an-introduction-with-applications-4th-edition.pdf