plot response for a step change in input

I am a little confused for a question, I have to modify code to see the response for a step change in input, should I be getting an oscillation where the waves 'fizzle' out, or a step like a square wave. zeta1 as to be between 1.0 >1.5, whilst zeta2: 0.0>1.0, with wn the natural frequency been varied code below:

y0=0.15 ; wn=1.44;

zeta1=3/(2*sqrt(2)); zeta2=1/(2*sqrt(2));

t=[0:0.1:10]; %

t1=acos(zeta1)*ones(1,length(t));

t2=acos(zeta2)*ones(1,length(t)); %

c1=(y0/sqrt(1-(zeta1*zeta1))); c2=(y0/sqrt(1-(zeta2*zeta2)));

y1=c1*exp(-zeta1*wn*t).*sin(wn*sqrt(1-(zeta1*zeta1))*t+t1);

y2=c2*exp(-zeta2*wn*t).*sin(wn*sqrt(1-(zeta2*zeta2))*t+t2);

bu=c2*exp(-zeta2*wn*t);bl=bu;

plot(t,y1,'-',t,y2,'-',t,bu,'-',t,bl,'-'),grid

xlabel('Time[sec]'),ylabel('y(t) Displacement[m]')

text(0.2,0.85,['overdamped zeta1=',num2str(zeta1)],'sc')

text(0.2,0.80,['underdamped zeta2=',num2str(zeta2)],'sc')

should I get rid of the 'grid' and replace with 'step' at the end of the plot. thanks

Answer 1

[Youssef Khmou]

Jason, You did not give details about the nature of the system, ( low pass, high pass,...). The Fourier transform of the square wave ( beginning of step) is cardinal sinusoidal , so your code seems correct to me.