02 Ot20 2. For the problem of forced vibration considered in class: 32V202V_ z = P.8(t)(x - L/2); V(x,0) = 0; *(x,0) = 0; V(0,t) = V(L, t) = 0 plot the solution for V(x, t) at various times in the vibration cycle using the Matlab script provided. Lav %Separation of variables Solution V(x, t) of Wave Equation % for vibration of a taut string with (OL/2 ? % Solution: V(x, t) = ? Ak*cos((2*k-1)*?*c*t/L)*sin((2*k-1)*?*x/L) k=1 Ak = 2*a0*(-1)^(k-1)/(2*k-1)^2/pi^2 L=1;a0=1;c=1; x=linspace(0, 1, 100);% location x along string t=linspace(0, 1, 11);%time steps when you want to see displacment V(x, t) [X, T]=meshgrid(x, t); V=zeros(size()); for k=1:20 Ak = 2*20*(-1)^(k-1)/(2*k-1)^2/pi12; V=V+AK* cos((2k-1)*pi*c*T/L). *sin((2*k-1)*pi*X/L); end figure(1) plot([0 0.5 1],[0 0.25 0], 'r',x,V(1, :), 'k',[01],[0 0], 'k--', 'linewidth', 2) xlabel('x');y label('V(x,0)'); title('Initial condition V(x,0)') legend('Series Approximtion', 'Actual Shape') figure(2) plot(x,V, [ 1],[0 0], 'k', 'linewidth', 2) axis ([0,1, -25,.25]) legendcell = strcat('t=', string(num2cell(t))); legend(legendCell); xlabel('x');ylabel('V(x, t)'); title('displacement vix, t) as function of time') 02 Ot20 2. For the problem of forced vibration considered in class: 32V202V_ z = P.8(t)(x - L/2); V(x,0) = 0; *(x,0) = 0; V(0,t) = V(L, t) = 0 plot the solution for V(x, t) at various times in the vibration cycle using the Matlab script provided. Lav %Separation of variables Solution V(x, t) of Wave Equation % for vibration of a taut string with (OL/2 ? % Solution: V(x, t) = ? Ak*cos((2*k-1)*?*c*t/L)*sin((2*k-1)*?*x/L) k=1 Ak = 2*a0*(-1)^(k-1)/(2*k-1)^2/pi^2 L=1;a0=1;c=1; x=linspace(0, 1, 100);% location x along string t=linspace(0, 1, 11);%time steps when you want to see displacment V(x, t) [X, T]=meshgrid(x, t); V=zeros(size()); for k=1:20 Ak = 2*20*(-1)^(k-1)/(2*k-1)^2/pi12; V=V+AK* cos((2k-1)*pi*c*T/L). *sin((2*k-1)*pi*X/L); end figure(1) plot([0 0.5 1],[0 0.25 0], 'r',x,V(1, :), 'k',[01],[0 0], 'k--', 'linewidth', 2) xlabel('x');y label('V(x,0)'); title('Initial condition V(x,0)') legend('Series Approximtion', 'Actual Shape') figure(2) plot(x,V, [ 1],[0 0], 'k', 'linewidth', 2) axis ([0,1, -25,.25]) legendcell = strcat('t=', string(num2cell(t))); legend(legendCell); xlabel('x');ylabel('V(x, t)'); title('displacement vix, t) as function of time')