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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.

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1 Answer 1

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

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.

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