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

Given that its creation in 1984, MATLAB's ever-growing recognition and performance have secured its place as an industry-standard software program package deal. The common, interactive setting of MATLAB 6.x, which incorporates a high-level programming language, flexible images features, and abundance of intrinsic features, is helping clients specialize in their purposes instead of on programming mistakes. MATLAB has now leapt some distance sooner than FORTRAN because the software program of selection for engineering purposes.

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**Extra info for Advanced Mathematics and Mechanics Applications Using MATLAB**

**Example text**

67, 1], yd = [0, 0, −1, 0, 0]. The program reads the wave speed, the string length, and data points specifying the initial deßection. The solution is evaluated for a range of x, t values. 10, which is a three-dimensional plot of traces of the string deßection for a sequence of times. 33. 25. Finally, a function to animate the solution over two motion cycles illustrates how the initial deßection splits, translates, and reßects from the boundaries. 13: Motion Trace Over a Short Time Interval © 2003 by CRC Press LLC MATLAB Example Program strngrun 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: function strngrun(rundemo) % % strngrun(rundemo) % ~~~~~~~~~~~~~~~~ % This function illustrates propagation of % waves in a tightly stretched string having % given initial deflection.

User inline functions used: % cbp, Ylsq, yexact 10: 11: 12: 13: % Function for Chebyshev data points cbp=inline([’(a+b)/2+(a-b)/2*cos(pi/n*’,... ’(1/2:n))’],’a’,’b’,’n’); 14: 15: 16: 17: 18: % Polynomial of degree n to least square fit % data points in vectors xd,yd Ylsq=inline(’polyval(polyfit(xd,yd,n),x)’,... ^p)’,’p’,’x’); 22: 23: 24: 25: 26: 27: 28: % Set data parameters. Functions linspace and % cbp generate data with even and Chebyshev % spacing n=10; nd=n+1; a=-4; b=4; p=2; xeven=linspace(a,b,nd); yeven=yexact(p,xeven); xcbp=cbp(a,b,nd); ycbp=yexact(p,xcbp); 29: 30: 31: nlsq=501; % Number of least square points xlsq=linspace(a,b,nlsq); ylsq=yexact(p,xlsq); 32: 33: % Compute interpolated functions for plotting © 2003 by CRC Press LLC 34: 35: 36: 37: 38: xplt=linspace(0,b,121); yplt=yexact(p,xplt); yyeven=Ylsq(xeven,yeven,n,xplt); yycbp=Ylsq(xcbp,ycbp,n,xplt); yylsq=Ylsq(xlsq,ylsq,n,xplt); yyspln=spline(xeven,yeven,xplt); 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: 56: 57: 58: 59: 60: 61: 62: 63: 64: 65: % Plot results j=6:nd; % Plot only data points for x>=0 plot(xplt,yplt,’-’,xplt,yyeven,’--’,...

7 Example of Waves in an Elastic String One-dimensional wave propagation is illustrated well by the response of a tightly stretched string of Þnite length released from rest with given initial deßection. The transverse deßection y(x, t) satisÞes the wave equation a2 yxx = ytt and the general solution for an inÞnite length string, released from rest, is given by y(x, t) = [F (x − at) + F (x + at)]/2 where F (x) is the initial deßection for −∞ < x < ∞. The physical interpretation for this equation is that the initial deßection splits in two parts translating at speed a,with one part moving to the right and the other moving to the left.

### Advanced Mathematics and Mechanics Applications Using MATLAB by David Halpern, Howard B. Wilson, Louis H. Turcotte

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