m = 500;    w = 3.2*pi;               % mass and desired omega_0
g = logspace(0,5,1000);               % take logarithmic steps for gamma
l = -g/(2*m);                         % decay rate lamdba
mu = sqrt(w^2 - l.^2);                % quasi-freq, note elementwise .^
r1 = l + i*mu; r2 = l - i*mu;         % matlab can do complex #s too!
figure; plot([r1,r2], '+');           % stack row vectors to plot both roots
xlabel('Re[r]'); ylabel('Im[r]');
axis equal; axis([-30 0 -15 15]);     % scale axes to show semicircle
