Vibrating beam concept question

[Dustinsfl]

If we had a beam fixed at $x = 0$ and on pin rollers at $x = L$, why would $u_{xx}(L,t) = 0$ and $u_x(0,t) = 0$.

$u(0,t) =0$ since the at $x = 0$ the beam is fixed and $u(L,t) = 0$ since the beam is on roller and wouldn't have any displacement, correct?

 

[Aaron Bex]

Yes, this is correct. $u_x(0,t) = 0$ means that the beam has no velocity at the fixed end, and $u_{xx}(L,t) = 0$ means that the beam has no acceleration at the roller end.