That's what I'm confused about. I know that I can express the motion of a vibrating string using sin and cos terms, but I don't know what BC's to apply if the ends of the string are free to move.
I want to express the shape of a string using sin and cos, but I am not sure what combination of terms is appropriate here.
Would y=Acos(kxwt) + Bcos(kx+wt) + Csin(kxwt) + Dsin(kx+wt) fully describe the motion?
