By Howard B. Wilson, Louis H. Turcotte, David Halpern
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Extra info for Adv Math Mech App using MatLab Book
Introducing a function g(x) such that g(x) = f (x), 0 ≤ x ≤ l and g(x) = −f (2l − x), l < x ≤ 2l leads to F (x) = sign(x)g(rem(abs(x), 2l)) where the desired periodicity is achieved using the MATLAB remainder function, rem. This same problem can also be solved using a Fourier sine series (see chapter 9). For the present we concentrate on the solution just obtained. A program was written to implement the translating wave solution when f (x) is a piecewise linear function computed using interp1. The system behavior can be examined from three different aspects.
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-’,...
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.
Adv Math Mech App using MatLab Book by Howard B. Wilson, Louis H. Turcotte, David Halpern