Posted by Steve Simon on April 28, 2015, 12:16 pm, in reply to "Trying to excite beyond max frequency in a monatomic chain"
Yes, this is correct. You might think y=sin(x) has no solution for y > 1, but it does if you allow x to be complex. If you find a complex k, just plug it into x_n = A e^{i w t  i k n a} and find a solution that decays with n. 
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