Need help with an integral interval

hey i have this matlab script that work fine, but i found out that my interval is wrong now i integrate from -d to a. in real i need from -d to a*sin(w*t) where d,a and w is known but t is variable or linspace from 0 to 30. see script bellow: PS need to change F at the bottom.

clear all
clear variables 
clc

H100 = 28.6083;              % Intermediate Water 
C100 = 17.8718;

Tmin = 13.6365;
Tmax = 17.7395;
Tmean = 15.6880;

%--------------------------------------------------------------------------
d = 100;                  % water depth
T = Tmin;                 % wave period 
a = H100/2;    % or C100  % wave amplitude
g = 9.81;                 % acceleration of gravity             
                          % x = direction of propagation
                          % t = time
w = 2*pi/T;               % wave frequency

syms k
k1 = solve(g*k*tanh(k*d)-w^2 == 0, k);
k = sqrt(k1.^2);                             % wave number                   
L = simple(((g*T.^2)*tanh(k*d))/(2*pi));     % wave length

% Morison equation data
D = 1;     % Diameter on column: D = 1m= drag, D = 5m= drag/mass, and D = 20m= mass 
p = 1025;
Cm = 2;
Cd = 1.1;

%--------------------------------------------------------------------------
% Velocity = V   % Acceleration = A
t = linspace(0,30);
x = 0;

syms z
V1 = (((a*k*g*cosh(k*(z+d)))/(w*cosh(k*d)))*sin(w*t-k*x));                % Extrapolation above free surface
V2 = ((a*k*g*cosh(k*(((z-a)/(1+a/d))+d)))/(w*cosh(k*d))*sin(w*t-k*x));    % Wheeler stretching
V3 = (((a*k*g*cosh(k*(0+d)))/(w*cosh(k*d)))*sin(w*t-k*x));                % z = 0 constant value used for surface   

A1 = ((a*k*g*cosh(k*(z+d)))/(cosh(k*d)))*cos(w*t-k*x);                    % Extrapolation above free surface
A2 = ((a*k*g*cosh(k*(((z-a)/(1+a/d))+d)))/(cosh(k*d)))*cos(w*t-k*x);      % Wheeler stretching
A3 = ((a*k*g*cosh(k*(0+d)))/(cosh(k*d)))*cos(w*t-k*x);                    % z = 0 constant value used for surface

%--------------------------------------------------------------------------
% Tmin for H100

Fm = (pi*p*Cm*A1*D.^2)/4;
Fd = ((p*Cd*D)/2)*V1.*(abs(V1));
F = int(Fm,z,-d,a*t)+int(Fd,z,-d,a*t);
[MaxValue_H100_Tmin_Extr, Index_At_F] = max(double(F))
t_Position_of_MaxValue_H100_Tmin_Extr = t(Index_At_F)

% i need to write somthing like( see bellow): but this makes an error.

%a1 = a*sin(w*t);
%F = int(Fm,z,-d,a1)+int(Fd,z,-d,a1);

[Konstantinos Sofos]

What is the error? May you have to debug your script, so that you can understand what is going wrong with the dimensions...

MATLAB Debugging Tutorial

[ekko ekkosen]

i can shorten my script see it got some errors inn it when i copyed it:

clear all
clear variables 
clc

H100 = 28.6083;              % Intermediate Water 
Tmin = 13.6365;

%--------------------------------------------------------------------------
d = 100;                  % water depth
T = Tmin;                 % wave period 
a = H100/2;    % or C100  % wave amplitude
g = 9.81;                 % acceleration of gravity             
                          % x = direction of propagation
                          % t = time
w = 2*pi/T;               % wave frequency

syms k
k1 = solve(g*k*tanh(k*d)-w^2 == 0, k);
k = sqrt(k1.^2);                             % wave number                   
L = simple(((g*T.^2)*tanh(k*d))/(2*pi));     % wave length

% Morison equation data
D = 1;      
p = 1025;
Cm = 2;
Cd = 1.1;

%--------------------------------------------------------------------------
% Velocity = V   % Acceleration = A
t = linspace(0,30);
x = 0;

syms z
V1 = (((a*k*g*cosh(k*(z+d)))/(w*cosh(k*d)))*sin(w*t-k*x));
A1 = ((a*k*g*cosh(k*(z+d)))/(cosh(k*d)))*cos(w*t-k*x);            

%--------------------------------------------------------------------------
% Tmin for H100

Fm = (pi*p*Cm*A1*D.^2)/4;
Fd = ((p*Cd*D)/2)*V1.*(abs(V1));
F = int(Fm,z,-d,a)+int(Fd,z,-d,a);
[MaxValue_H100_Tmin_Extr, Index_At_F] = max(double(F))
t_Position_of_MaxValue_H100_Tmin_Extr = t(Index_At_F)

every thing works fine above, but i wont to change the end interval of my integrals. see F has integral to a. i wont to change this to:

%a1 = a*sin(w*t);
%F = int(Fm,z,-d,a1)+int(Fd,z,-d,a1);

but this makes an error saying:

Error using mupadmex
Error in MuPAD command: The argument is invalid. [Dom::Interval::new]

Error in sym/int (line 124)
   rSym = mupadmex('symobj::intdef',f.s,x.s,a.s,b.s,options);

Error in ekko (line 50)
F = int(Fm,z,-d,a1)+int(Fd,z,-d,a1);

[Konstantinos Sofos]

To eval symbolic expressions to specific values of the symbolic variables you can try

F = eval('int(Fm,z,-d,a1)+int(Fd,z,-d,a1)')

[ekko ekkosen]

F = eval('int(Fm,z,-d,a1)+int(Fd,z,-d,a1)')

dosent work for me.