It has part of the analysis of the problem wrong. Can anyone spot it!
Renault and Tyler go astray by assuming that the potential energy is
given by 1/2 kx^2, which is incorrect because the stretching isn't
linear. They effectively rederive the standard "add 1/3 of the mass
of the spring" result, which is a good approximation for small spring
masses precisely because, in that case, the stretching *is* almost
linear, but begins to fail for large spring masses as in this
problem. A proper solution must correctly account for the fact that
the spring is an elastic medium which can support numerous modes of
oscillation, only one of which is the usual fundamental mode.
The difference between the correct solution and Renault and Tyler's
"add 1/3 of the mass of the spring" approximation is less than a
percent as my solution shows.
It also turns out that this problem was discussed at length in the
pages of AJP some forty years ago.