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By David Halpern, Howard B. Wilson, Louis H. Turcotte

Considering the fact that its creation in 1984, MATLAB's ever-growing attractiveness and performance have secured its place as an industry-standard software program package deal. The ordinary, interactive setting of MATLAB 6.x, which incorporates a high-level programming language, flexible images features, and abundance of intrinsic capabilities, is helping clients concentrate on their functions instead of on programming error. MATLAB has now leapt a ways sooner than FORTRAN because the software program of selection for engineering functions.

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7: Partial Motion Trace for Pendulum Almost Pushed Over the Top © 2003 by CRC Press LLC Program pendulum 1: 2: 3: 4: 5: 6: 7: 8: function pendulum(rundemo) % pendulum(rundemo) % This example analyzes damped oscillations of % a simple pendulum and animates the motion. 2*theta’(t)+sin(theta) = 0 9: 10: 11: 12: % Type pendulum with no argument for inter% active input. 2*theta’’(t)+sin(theta) = 0’) 23: 24: 25: 26: 27: % Create an inline function defining the % differential equation in matrix form zdot=inline(...

Poly. for Even Spacing’,... ’Spline Curve’,... ’Interpolation Points’,2) title([’SPLINE CURVE AND POLYNOMIAL ’,... ’USING EVEN SPACING’]) xlabel(’x axis’), ylabel(’function values’) % print(gcf,’-deps’,’splpofit’) shg, pause plot(xplt,yplt,’-’,xplt,yycbp,’--’,... ’,xcbp(j),ycbp(j),’s’,... ’linewidth’,2) legend(’Exact Function’,... ’Poly. for Chebyshev Points’,... ’Least Square Poly. Fit’,... ’Interpolation Points’,1) title([’LEAST SQUARE POLY. AND POLY. ’,... 4 Conformal Mapping Example This example involves analytic functions and conformal mapping.

8 shows x(t) for the default data case. The input data values for this case use [m, c, k, f1 , f2 , w, x0 , v0 , tmax, nt] <=> [1, 3, 1, 1, 0, 2, 0, 2, 30, 250]. Note that near t = 11 , the transient and forced solution components interact so that the block almost pauses momentarily. However, the solution then quickly approaches the steady state. 9 shows the Þnal position of the mass and the applied force at the end of the chosen motion cycle. 9: Block Sliding On a Plane with Viscous Damping © 2003 by CRC Press LLC 30 Program smdplot 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: function [t,X,m,c,k,f1,f2,w,x0,v0]= smdplot(example) % % [t,X,m,c,k,f1,f2,w,x0,v0]= smdplot(example) % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ % This function plots the response and animates the % motion of a damped linear harmonic oscillator % characterized by the differential equation % m*x’’+c*x’+k*x=f1*cos(w*t)+f2*sin(w*t) % with initial conditions x(0)=x0, x’(0)=v0.

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