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

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43: 44: 45: [x0,v0]=inputv(... ’Input x0, v0 (try 0, 2) >> ? ’); 46: 47: 48: 49: [tmax,nt]=inputv(... ’Input tmax, nt (try 30, 250) >> ? ’); end 50: 51: 52: t=linspace(0,tmax,nt); X=smdsolve(m,c,k,f1,f2,w,x0,v0,t); 53: 54: 55: 56: 57: 58: 59: 60: 61: % Plot the displacement versus time plot(t,X,’k’), xlabel(’time’) ylabel(’displacement’), title(... 5*f; fa=abs(f); sf=sign(f); xj=x(j,:); xmaxj=max(xj); if sf>0 xforc=xmaxj+[0,fa,fa+xtip]; © 2003 by CRC Press LLC 87: 88: 89: else xforc=xmaxj+[fa,0,-xtip]; end 90: 91: 92: 93: 94: 95: 96: 97: 98: 99: 100: 101: 102: % Plot the spring, block, and force % plot(xj,y,rx,ry,’k’,xforc,ytip,’r’) %plot(xj,y,’k-’,rx,ry,’k-’,xforc,ytip,’k-’) plot(xj,y,’k-’,xforc,ytip,’k-’,...

1:30) > ? ’]); 42: 43: 44: 45: 46: 47: 48: disp(’ ’) titl=input(’Input a title for the graphs : ’,’s’); disp(’ ’), disp(... ’Input 1 to leave images of all positions shown’) trac=input(... ’in the animation, otherwise input 0 > ? 05) close, disp(’ ’), disp(’All Done’), disp(’ ’) 84: 85: end 86: © 2003 by CRC Press LLC 87: %=============================================== 88: 89: 90: 91: 92: 93: 94: 95: 96: 97: 98: 99: 100: 101: 102: 103: 104: 105: 106: function animpen(t,th,titl,tim,trac) % % animpen(t,th,titl,tim,trac) % ~~~~~~~~~~~~~~~~~~~~~~~~~~ % This function plots theta versus t and animates % the pendulum motion % % t - time vector for the solution % th - angular deflection values defining the % pendulum positions % titl - a title shown on the graphs % tim - a time delay between successive steps of % the animation.

The system behavior can be examined from three different aspects. 1) The solution y(x, t) for a range of x and t values describes a surface. 2) The deßection curve at a particular time t 0 is expressed as y(x, t0 ), 0 < x < l. 3) The motion history at a particular point x 0 is y(x0 , t), t ≥ 0. The nature of F (x) implies that the motion has a period of 2l/a. Waves striking the boundary are reßected in inverted form so that for any time y(x, t + l/a) = −y(x, t). 67, 1], yd = [0, 0, −1, 0, 0]. The program reads the wave speed, the string length, and data points specifying the initial deßection.

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Adv Math Mech App using MatLab Book by Howard B. Wilson, Louis H. Turcotte, David Halpern


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