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.