# Resonance and standing waves on a bar [closed]

I'm having trouble solving this problem:

By applying a harmonic force, acting on the end of a free bar of length $$L$$, a standing wave is formed due to multiple reflections:

• Where are the nodes of the tensile stresses in it? What will be the amplitude of the driving force $$F_o$$, if the amplitude of the tensile stresses in the standing wave is $$\sigma_o$$ and the cross section of the bar is $$S$$ ?
• Plot the resonance curve (the graph of the dependence of $$\dfrac{\sigma_o S}{F_o}$$ with respect to the frequency $$\omega$$ of the driving force). For what frequencies are harmonic oscillations possible in the absence of the driving force?

I know that the driving force should be $$F=F_o\sin\omega t$$ and that somehow, Hooke's law is applied. After that, I don't know any way to approach the problem.

## 1 Answer

Well, i think i can help a little, see this image:

If it helps you to construct a equation:

$$\frac{F}{A} = Y\frac{\partial \varepsilon }{\partial x}$$

I think is enough to answer the question with this, being epsilon the wave function.