Plot all four functions

I need help. I have my four functions and if I run my code it only plots the first response not all four. Furthermore I don't know how to have all four plots on the same frame.

Thank you.

%% Givens
m=2; %kg
k=200; %N/m
x0=0.05; %meters
x_dot=2; %m/s
%% Solution Part A
Wn= (k/m)^0.5;
c= (2*m*Wn);
Cc= (2*m*Wn);
Zeta= c/Cc
%% Solution Part B
if Zeta==1
    C1=x0;
    C2=x_dot+Wn*x0;
    x =  @(t) (C1+C2*t)*exp(-Wn*t)
    fplot(x,[0,1])
end
if Zeta==0
    X= (((x0^2)*(Wn^2)+(x_dot^2)+(2*x0*x_dot*Zeta*Wn))^0.5)/(((1-(Zeta^2))^0.5)*Wn);
    phi= atan((x_dot+(Zeta*Wn*x0))/(x0*Wn*((1-(Zeta^2))^0.5)));
    Wd= ((1-(Zeta^2))^0.5)*Wn;  
    x = @(t) X*(exp(-Zeta*Wn*t))* cos((Wd*t)-phi)
    fplot(x,[0,1])
end
if Zeta==0.5
    X= (((x0^2)*(Wn^2)+(x_dot^2)+(2*x0*x_dot*Zeta*Wn))^0.5)/(((1-(Zeta^2))^0.5)*Wn);
    phi= atan((x_dot+(Zeta*Wn*x0))/(x0*Wn*((1-(Zeta^2))^0.5)));
    Wd= ((1-(Zeta^2))^0.5)*Wn;  
    x = @(t) X*(exp(-Zeta*Wn*t))* cos((Wd*t)-phi)
    fplot(x,[0,1])
end
if Zeta==2
    C1=x0;
    C2=x_dot+Wn*x0;
    x= @(t) C1*exp(-Zeta+sqrt(Zeta^2-1)*Wn*t)+C2*exp(-Zeta-sqrt(Zeta^2-1)*Wn*t)
    fplot(x,[0,1])
end    
%% Solution Part C

Answer 1

[Aquatris]

It only plots the first one because your Zeta is always 1 (c/cc = 1). Moreover, even if you changed Zeta to be other values, it would overwrite your graph since you do not have "hold on" for the figure.

instead of using if statements, why dont you define 4 different functions like this:

clear,clc

%% Givens
m=2; %kg
k=200; %N/m
x0=0.05; %meters
x_dot=2; %m/s
%% Solution Part A
Wn= (k/m)^0.5;
c= (2*m*Wn);
Cc= (2*m*Wn);
%% Solution Part B
Zeta=1;
C1=x0;
C2=x_dot+Wn*x0;
x_1 =  @(t) (C1+C2*t)*exp(-Wn*t);

Zeta=0;
X= (((x0^2)*(Wn^2)+(x_dot^2)+(2*x0*x_dot*Zeta*Wn))^0.5)/(((1-(Zeta^2))^0.5)*Wn);
phi= atan((x_dot+(Zeta*Wn*x0))/(x0*Wn*((1-(Zeta^2))^0.5)));
Wd= ((1-(Zeta^2))^0.5)*Wn;
x_0 = @(t) X*(exp(-Zeta*Wn*t))* cos((Wd*t)-phi);

Zeta=0.5;
X= (((x0^2)*(Wn^2)+(x_dot^2)+(2*x0*x_dot*Zeta*Wn))^0.5)/(((1-(Zeta^2))^0.5)*Wn);
phi= atan((x_dot+(Zeta*Wn*x0))/(x0*Wn*((1-(Zeta^2))^0.5)));
Wd= ((1-(Zeta^2))^0.5)*Wn;
x_05 = @(t) X*(exp(-Zeta*Wn*t))* cos((Wd*t)-phi);

Zeta = 2;
C1=x0;
C2=x_dot+Wn*x0;
x_2= @(t) C1*exp(-Zeta+sqrt(Zeta^2-1)*Wn*t)+C2*exp(-Zeta-sqrt(Zeta^2-1)*Wn*t);

figure(1)
fplot(x_0,[0 1],'b')
hold on
fplot(x_05,[0 1],'r')
fplot(x_1,[0 1],'g')
fplot(x_2,[0 1],'k')
hold off
legend('Zeta = 0','Zeta = 0.5','Zeta = 1','Zeta = 2')
axis([0 1 -0.5 0.5])
%% Solution Part C

This way you can plot them all.

Answer 2

[darova]

Please use hold on

[Areg Arzoomanian]

how would I integrate that into my code? Please elaborate. Thank you for your fast response.