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

On account that its advent in 1984, MATLAB's ever-growing recognition and performance have secured its place as an industry-standard software program package deal. The basic, interactive setting of MATLAB 6.x, which incorporates a high-level programming language, flexible pictures functions, and abundance of intrinsic capabilities, is helping clients specialize in their functions instead of on programming mistakes. MATLAB has now leapt a ways prior to FORTRAN because the software program of selection for engineering purposes.

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History is to be evaluated (try len/4) > ? ’); disp(’ ’) disp(’Specify time t=t0 when the deflection’) t0=input(’curve is to be plotted > ? ’); disp(’ ’) titl=input(’Input a graph title > ? 33*len/a; titl=’TRANSLATING WAVE OVER HALF A PERIOD’; end 61: 62: nx=80; x=0:len/nx:len; t=0:tmax/nt:tmax; 63: 64: 65: h=max(abs(yd)); xplot=linspace(0,len,201); tplot=linspace(0,max(t),251)’; 66: 67: 68: 69: 70: 71: [Y,X,T]=strngwav(xd,yd,x,t,len,a); plot3(X’,T’,Y’,’k’); xlabel(’x axis’) ylabel(’time’), zlabel(’y(x,t)’), title(titl) if pltsav, print(gcf,’-deps’,’strngplot3’); end drawnow, shg, disp(’ ’) 72: 73: 74: disp(’Press return to see the deflection’) disp([’when t = ’,num2str(t0)]), pause 75: 76: 77: 78: 79: 80: 81: 82: [yt0,xx,tt]=strngwav(xd,yd,xplot,t0,len,a); close; plot(xx(:),yt0(:),’k’) xlabel(’x axis’), ylabel(’y(x,t0)’) title([’DEFLECTION WHEN T = ’,num2str(t0)]) axis([min(xx),max(xx),-h,h]) if pltsav, print(gcf,’-deps’,’strngyxt0’); end drawnow, shg 83: 84: 85: disp(’ ’) disp(’Press return to see the deflection history’) © 2003 by CRC Press LLC 86: disp([’at x = ’,num2str(x0)]), pause 87: 88: 89: 90: 91: 92: 93: 94: 95: yx0=strngwav(xd,yd,x0,tplot,len,a); plot(tplot,yx0,’k’) xlabel(’time’), ylabel(’y(x0,t)’) title(...

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-’,...

The initial conditions given by this particular solution are X(0) = real(F ) and X (0) = real(i ω F ). The characteristic equation for the homogeneous equation is m s2 + c s + k = 0 which has roots s1 = (−c + r)/(2m), s2 = (−c − r)/(2m), r = c2 − 4m k. Then the homogeneous solution has the form u(t) = d(1) exp(s1 t) + d(2) exp(s2 t) where d = [1, 1; s1 , s2 ] \ [x0 − X(0); v0 − X (0)] and the complete solution is x(t) = u(t) + X(t). © 2003 by CRC Press LLC A couple of special cases arise. , c = 0, ω = k/m.

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