- #1

LCSphysicist

2020 Award

- 432

- 110

- 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:

First:

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.

Second:

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.