- Homework Statement:
- I will post an image right below.
- Relevant Equations:
- All below.
I am trying to solve this question by ξ = A*cos(ωt + θ)*sin(kx + Φ)
Anyway, the two initial terms of the product helps nothing (i think), what matters is sin(kx + Φ)
So, i tried by two ways:
The stress is essentially zero on the ends, that is, something like cte*∂ξ/∂x (strain) would be zero, so
L is the length of the rod.
cos(kx + Φ) need to be 0
Φ = (2n-1)*π
kL + Φ = (2n-1)*π
It is not good.
The half length position would carry a node, so
ξ = A*cos(ωt + θ)*sin(kL/2 + Φ) = 0
KL/2 + Φ = (n)*π
and with this i can not solve without Φ in the expression.