1. NoViC, Dept. of Mechanical Eng. 2016. 03. 17

2. Acoustics Lab., NoViC 1. Download Matlab 2

3. Acoustics Lab., NoViC Activation Key 17925-02416-09128-40758-01531 2. Create “Mathworks” account 3

4. Acoustics Lab., NoViC 3. Installation 4 Matlab default view 1 2 3 4 5 6

5. Acoustics Lab., NoViC 1. Input variables and operations (1/5) 5 >> a = 1 a = 1 >> b = 2 b = 2 Command Window >> a + b ans = 3 >> a - b ans = >> a * b ans = 2 >> a / b ans = 0.5000  4 fundamental arithmetic operations  Scalar input (real value) Command Window + : Addition - : Subtraction * : Multiplication / : Division  Priority of operation: (*, /) > (+, -) >> a + b / a - b ans = 1 >> (a + b) / (a - b) ans = -3 Command Window  Square operation (^) >> a^5 (when a=2) ans = 32 >> a^5+1 ans = 33 >> a^(5+1) ans = 64 Command Window

6. Acoustics Lab., NoViC 1. Input variables and operations (2/5) 6 >> c = a+j*b c = 1.0000 + 2.0000i >> c = a+i*b c = 1.0000 + 2.0000i Command Window  Scalar input (complex value) i or j : complex variable  Trigonometric functions >>x = 45/180*pi x = 0.7854 >> sin(x) ans = 0.7071 >> cos(x) ans = 0.7071 Command Window  Complex operations >> real(c) ans = 1 >> imag(c) ans = 2 >> conj(c) ans = 1.0000 - 2.0000i >> abs(c) ans = 2.2361 >> angle(c) ans = 1.1071 Command Window real(c): real value of c imag(c): image value of c conj(c): complex conjugate of c abs(c): absolute value of c angle(c): phase value of c >> tan(x) ans = 1.0000 >> exp(j*x) ans = 0.7071 + 0.7071i Real Im  1-2i 1 2

7. Acoustics Lab., NoViC 1. Input variables and operations (3/5) 7 >> A=[1 2; 3 4] A = 1 2 3 4 >> B=[3 5; 7 9] B = 3 5 7 9 >> C = [1; 5] Command Window  Matrix and vector input  Matrix-matrix operation >> A + B ans = 4 7 10 13 >> A - B ans = -2 -3 -4 -5 Command Window >> C = [1 5]' C = 1 5 >> D = [2 3] D = 2 3 >> E = [1:2:9] E = 1 3 5 7 9 ; (semicolon): Changing the row : (colon): Pick out selected row ‘ (inverted comma): Transpose operator >> A * B ans = 17 23 37 51 >> A^3 ans = 37 54 81 118 >> A*C ans = 1 5 >> D*A ans = 11 16 Command Window  Matrix-vector/scalar operation >> A*5 ans = 5 10 15 20 >> A/2 ans = 0.5 1.0 1.5 2.0

8. Acoustics Lab., NoViC 1. Input variables and operations (4/5) 8 Command Window  Other matrix operations >> transpose(A) ans = 1 3 2 4 >> det(A) ans = -2 >> inv(A) ans = -2.0000 1.0000 1.5000 -0.5000 >> A * inv(A) ans = 1.0000 0.0000 0.0000 1.0000 >> [V,D] = eig(A) V = -0.8246 -0.4160 0.5658 -0.9094 D = -0.3723 0 0 5.3723 Command Window >> size(A) ans = 2 2 >> size(C) ans = 2 1 >> length(A) ans = 2 >> length(C) ans = 2 >> eye(2,2) ans = 1 0 0 1 >> zeros(1,2) ans = 0 0 >> ones(1,2) ans = 1 1 transpose(A)  same with ‘ (inverted comma) det(A)  Determinant of A matrix inv(A)  Inverse matrix of A matrix eig(A)  Eigenvalues and vectors V: Eigenvectors D: Eigenvalues size(A)  Size of A matrix length(A)  length of A matrix eye(m,n)  Make the mXn identity matrix zeros(m,n)  Make the mXn matrix of zeros ones(m,n)  Make the mXn matrix of ones

9. Acoustics Lab., NoViC 1. Input variables and operations (5/5) 9 Command Window  Comma for matrix computation >> A*B ans = 17 23 37 51 >> A.*B ans = 3 10 21 36 >> A^2 ans = 7 10 15 22 >> A.^2 ans = 1 4 9 16 Command Window >> x=[0:0.1:pi]; >> y=sin(x); ; (semicolon): hide the input/output variables variables save in the workspace  Function and vector General matrix multi. Element by element multi. General matrix multi. Element by element multi. Final value (Upper bound) Initial value (Lower bound) Step size X=[0 0.1 0.2 … 2.9 3.1] (Dimension: 1X32) Y=[0 0.0998..0.1411 0.0416] (Dimension: 1X32)

10. Acoustics Lab., NoViC 2. Plotting the graph (1/1) 10  Setting the variables (input and output values)  Plotting the figure >> figure(1) >> plot(x, y, 'r-') >> grid on >> xlabel('x [rad]') >> ylabel('sin(x)') >> title('sin function') Command Window >> x=[0:0.1:pi]; >> y=sin(x); figure(1)  numbering the figure Plot(x,y,’r-’)  x: x-axis data, y: y-axis data, ‘r-’: red solid line grid on  show the grid line on the figure To get the more information of plot, Input the help plot in command window Command Window >> help plot semilogx  x-axis is log scale semilogy  y-axis is log scale loglog  x, y-axes are log scale

11. Acoustics Lab., NoViC M-file making 11 F5 Dragging and select several statement +F9 key  Run only in the selected part F9

12. Acoustics Lab., NoViC 3. Iteration structure (1/2) 12 >> sum = 0; >> for n = 1:10 sum = sum + n; end >> sum sum = 55 Command Window  Example) sum of 1 to 10 for variable = int : n : final statement end Repeat the statement until the final variable Not convenient to use command window Open the editor Click F5 key  save the editor  Implement the MATLAB program

13. Acoustics Lab., NoViC 3. Iteration structure (2/2) 13  Example) sum of 1 to 10 while conditional statement statement end Repeat the statement until conditional statement is satisfied C.if loop  Example) sum of 1 to 10 if expression1 statement1 elseif expression2 statement2 else statement3 end Implement statement1 if expression1 is satisfied, Implement statement2 if expression1 is unsatisfied and expression2 is unsatisfied, Implement statement3 if expression 1 and 2 are unsatisfied

14. Acoustics Lab., NoViC 14 function xdot = sdof(t,x) xdot = zeros(2,1); xdot(1) = x(2); xdot(2) = -(2/3)*x(1) - (1/3)*x(2); 1. First-order form t0 = 0; tf = 20; x0 = [0 0.25]; [t, x] = ode45('sdof', [t0 tf], x0); plot(t,x(:,1),'linewidth',3); hold on; plot(t,x(:,2),'--r','linewidth',3); title('Example 1.9.2'); xlabel('Time'); ylabel('Displacement (solide) and velocity (dashed)'); grid on; sdof.m Tutorial_ode45.m where

15. Acoustics Lab., NoViC 15 1. Start matlab 2. input this code -> urlwrite('https://raw.githubuserconte nt.com/vibrationtoolbox/vtoolbox/ma ster/vtbud.m','vtbud.m'); 3. then input this code -> vtbud 4. Installation will be started You have to select the path where the function files are