- #1
RyanTG
- 13
- 0
I don't really understand boundary conditions and I've been trying to research it for ages now but to no real avail. I understand what boundary conditions are, I think. You need them along with the initial conditions of a wire/string in order to describe the shape of motion of the string. I guess giving a question example would reveal my lack of knowledge better than me trying to explain it:
1)A rope is held under tension, F. It lies along the x-axis when undisturbed. The mass
per unit length is l for x < 0 and r for x > 0. A wave-like disturbance is incident
from the right.
(i) Give and explain the origin of the boundary conditions on the displacement,
y(x), at x = 0.
I'm not entirely sure here? It is simply just: y(x=0,t) = 0? What about this x < 0 and x > 0 business, what does that explicitly mean? Does it give insight into whether or not the wire is fixed at both ends, fixed at only one end, attached to another wire etc etc?
What about for a string fixed at one end but not the other? Supposedly the answer is:
y(0; t) = [itex]\frac{\delta y}{\delta x}[/itex](L, t) = 0
What does this mean?
Thank you for your time.
1)A rope is held under tension, F. It lies along the x-axis when undisturbed. The mass
per unit length is l for x < 0 and r for x > 0. A wave-like disturbance is incident
from the right.
(i) Give and explain the origin of the boundary conditions on the displacement,
y(x), at x = 0.
I'm not entirely sure here? It is simply just: y(x=0,t) = 0? What about this x < 0 and x > 0 business, what does that explicitly mean? Does it give insight into whether or not the wire is fixed at both ends, fixed at only one end, attached to another wire etc etc?
What about for a string fixed at one end but not the other? Supposedly the answer is:
y(0; t) = [itex]\frac{\delta y}{\delta x}[/itex](L, t) = 0
What does this mean?
Thank you for your time.