Question: How to form equation of specific kind?

Hello,

I would like to create a function from an equation.
I have define 4 functions u[1](t), ..., u[4](t).
From these 4 functions, I would like to define 4 equations. I would like to obtain this result:
Equ[1]:=u[1](t)=L/2*cos(w*t+phi[1])
Equ[2]:=u[2](t)=L/2*cos(w*t+phi[2])
Equ[3]:=u[3](t)=L/2*cos(w*t+phi[3])
Equ[4]:=u[4](t)=L/2*cos(w*t+phi[4])

My code is the following:

for i to 4
do
u[i]:=unapply(L/2*cos(w*t+phi[i]),t);
Equ[i]:='u[i](t)'=u[i](t);
end do;

These lines are not working because the left member is not incremented (u[i](t) stays at each iteration u[i](t))

Generally, how can I transform a function to an equation ?
And, in this specific case, how can I obtain the four equations mentioned above ?

Thanks a lot for your help.