4B

a = 1;
gam = 0;
om0 = 5;
tmax = 10;
c = 1;

a1 = 0.5;
I1 = @(t) Impulse(t,c,a1);
options1 = odeset( 'MaxStep', a1 );
a2 = 0.25;
I2 = @(t) Impulse(t,c,a2);
options2 = odeset( 'MaxStep', a2 );
a3 = 0.05;
I3 = @(t) Impulse(t,c,a3);
options3 = odeset( 'MaxStep', a3 );
% a4 = 0.01;
% I4 = @(t) Impulse(t,c,a4);
% options4 = odeset( 'MaxStep', a4 );

[t15a,x15a] = ode15s( @(t,x) [x(2); I1(t) - om0^2*x(1) - 2*gam*x(2)], [0 tmax], [0; 0], options1 );
[t15b,x15b] = ode15s( @(t,x) [x(2); I2(t) - om0^2*x(1) - 2*gam*x(2)], [0 tmax], [0; 0], options2 );
[t15c,x15c] = ode15s( @(t,x) [x(2); I3(t) - om0^2*x(1) - 2*gam*x(2)], [0 tmax], [0; 0], options3 );
% [t15d,x15d] = ode15s( @(t,x) [x(2); I4(t) - om0^2*x(1) - 2*gam*x(2)], [0 tmax], [0; 0], options4 );

figure();
plot( t15a,x15a(:,1), t15b,x15b(:,1), t15c,x15c(:,1));
xlabel('t');
ylabel('y');
legend( 'a = 0.5', 'a = 0.25', 'a = 0.05');

%% 2

tsol = [0:.1:8];
[tsol,xsol]= ode45( @(t,x) [x(2); I1(t) - 2*gam*x(2)], [tsol], [0; 0] );
plot(tsol,xsol)