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Spherical stellar systems such as King models, in which the distributionfunction is a decreasing function of energy and depends on no other invariant,are stable in the sense of collisionless dynamics. But Weinberg showed, by aclever application of the matrix method of linear stability, that they may benearly unstable, in the sense of possessing {\sl weakly} damped modes ofoscillation. He also demonstrated the presence of such a mode in an $N$-bodymodel by endowing it with initial conditions generated from his perturbativesolution. In the present paper we provide evidence for the presence of thissame mode in $N$-body simulations of the King $W_0 = 5$ model, in which theinitial conditions are generated by the usual Monte Carlo sampling of the Kingdistribution function. It is shown that the oscillation of the density centrecorrelates with variations in the structure of the system out to a radius ofabout 1 virial radius, but anticorrelates with variations beyond that radius.Though the oscillations appear to be continually reexcited (presumably by themotions of the particles) we show by calculation of power spectra thatWeinberg's estimate of the period (strictly, $2\pi$ divided by the real part ofthe eigenfrequency) lies within the range where the power is largest. Inaddition, however, the power spectrum displays another very prominent featureat shorter periods, around 5 crossing times.

$l=1$: Weinberg's weakly damped mode in an $N$-body model of a spherical stellar system