plotting graph including sigma

I am trying to plot this equation.

I have the values of B, omega_d, zeta, N_k and t_j is the multiples of 1.89.

Below is what I tried but the plot is weird and I can't find what's wrong.

Any comment will be helpfull. Thanks!

B_n=-5.36 ;
omega_d= 400;
zeta=29 ;
N_k=10;
sum=0;

for i=1:N_k
    
    t_j= 1.89.*i;
    
    sum= sum+ exp(-(zeta/2).*(t-t_j)).*(-zeta*(sin(omega_d/2.*(t-t_j)))+ omega_d.*cos(omega_d/2*(t-t_j)));
    
end 
sum=B_n/omega_d.*sum;

t=0:10;
plot(t,sum)

[Walter Roberson]

We recommend against using sum as the name of a variable, as it is very common to find that in the same code one also needs to use sum as the name of a function.

[Walter Roberson]

t is not defined in this code.

Answer 1

[Walter Roberson]

Your total is pretty large at small times, and by comparison decays to nothing. This behaviour continues, with large oscillations that dampen quickly relative to earlier values

syms t
Q = @(v) sym(v);

B_n = Q(-536)/100;
omega_d = Q(400);
zeta = Q(29);
N_k = 10;

parts = zeros(1, N_k, 'sym');
for i=1:N_k    
    t_j= 1.89.*i;
    parts(i) = exp(-(zeta/2).*(t-t_j)).*(-zeta*(sin(omega_d/2.*(t-t_j)))+ omega_d.*cos(omega_d/2*(t-t_j)));  
end
total = B_n/omega_d.*sum(parts);

fplot(total, [0 2])

fplot(total, [8 10])

[Sojung Park]

Thank you so much!

I have an extra question. How can I change this code if there is a relation between N_k, t, t_j. The relation is that N_k is the integer of t/tt.(when I define t_j=tt*N_k)

I'm confused how I can get the each value when t is changing within the range and apply the effects on the other components.(I tried 'while' and 'if' but I got a warning messege 'Operands to the logical and (&&) and or (||) operators must be convertible to logical scalar values.')