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First one bin toppling because the torque about $X$ due to wind is greater than the torque about X due to the weight of the bin $W$. It depends from which direction the wind is blowing. If both bins are facing the wind I do not think it makes any difference if there is one bin or two. However if only one bin presents itself to the wind and the other is ...

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Looking at the problem apart from the "sloped driveway" aspect in your previous question... The rationale of putting the garbage bags side by side is similar to using an "I" beam for structural support. The wind force only acts directly on the first bag. The second bag has force from the first bag, but it's cut in half, since they end up sharing the wind ...

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This question is natural, and I needed to solve it for myself many years ago. I don't remember the derivation and don't have time to reproduce it, but at least in the case of $J=\rho=\sigma=0$ and fixed $\omega\neq 0$ the boundary conditions are not independent, and it is enough to require that tangential components of $E$ and $H$ are continuous at the ...

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In general, what we use for periodic boundary conditions is defined by $Y(0)=Y(L)$ and $\frac{dY}{dx}(0)=\frac{dY}{dx}(L)$. The sole condition $Y(0) = Y(L)$ I believe is not sufficient to impose conditions on $k$. This is due to the fact that when we talk about "periodic conditions", it is implied that the derivative is also periodic. Indeed since the ...

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For the strict boundary conditions, the -n solution is linearly dependent with the n solution: it's the same wavefunction multiplied by -1. $\psi_{-n}(x)=\sin(-n\frac\pi Lx) = -\sin(n\frac\pi Lx)=-\psi_{n}(x)$

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