...suppose a beam, simply supported, length = L, etc..
Let's consider the 3 first modes (N=3)
The modal response is something like this :
P(x) = A1*sin(pi*x/L) + A2*sin(pi*2*x/L) + A3*sin(pi*3*x/L). (Sum of the 3 modes)
You can imagine P(x) (for all x) as just 1 point of coordinates (A1,A2,A3)...