Vibrating String: Interpreting ∂u/∂x(L,t)=0 Boundary Condition

[prehisto]

Homework Statement

(∂^2 u)/(∂t^2 )=a^2 (∂^2 u)/(∂x^2 ) x∈(0,l) t>0
u(0,t)=0 ; ∂u/∂x(L,t)=0
u(x,o)=u1; ∂u/∂t(x,o)=x

I can not figure out physical interpretation of boundary condition ∂u/∂x(L,t)=0, what does it mean. Can someone can help me with this ?

Homework Equations

The Attempt at a Solution

 

[dikmikkel]

The string is clamped at L and 0. So its amplitude is 0 there.

 

[clamtrox]

That's not true. ∂u/∂x(L,t)=0 means that the string is always perpendicular to the wall at the other endpoint. So you can think a very relaxed string being attached to a pole, sliding along it without friction.

 

[prehisto]

Thanks.

 

[Morgoth]

One way to understand what is it each time, is:
1. Know what derivatives in your problem mean.
2. See how it affects your solution after you bring them in it.