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

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

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One pair per line)’]) for j=2:n+1,[xd(j),yd(j)]=inputv; end; disp(’ ’) disp(’Input tmax and the number of time steps’) [tmax,nt]=inputv(’(Try len/a and 40) > ? ’); disp(’ ’) © 2003 by CRC Press LLC 41: 42: 43: 44: 45: 46: 47: 48: disp(’Specify position x=x0 where the time’) x0=input(... ’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(...

Solving the general case requires elliptic functions seldom encountered in routine engineering practice. Nevertheless, the pendulum equation can be handled very well for general cases by numerical integration. © 2003 by CRC Press LLC Suppose a bar of negligible weight is hinged at one end and has a particle of mass m attached to the other end. The bar has length l and the deßection from the vertical static equilibrium position is called θ. Assuming that the applied forces consist of the particle weight and a viscous drag force proportional to the particle velocity, the equation of motion is found to be θ (τ ) + c g θ (t) + sin(θ) = 0 m l where τ is time, c is a viscous damping coefÞcient, and g is the gravity constant.

Disp(’ ’) © 2003 by CRC Press LLC 41: 42: 43: 44: 45: 46: 47: 48: disp(’Specify position x=x0 where the time’) x0=input(... ’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(...

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