Besides @Jan's equations, maybe there's a way that's a bit more intuitive, or not. In simple terms, the three ways a system can respond to an impulse response is with an exponentially decaying output (oscillatory, or not), an stable oscillation, or a divergent output (oscillatory, or not). Since we're talking about a passive system, there is no divergence, because there's no way you can have a positive real part of a pole in there. So there can be only a decaying output, or an oscillation. In order for the latter to happen, you must have ideal L and C, and no R. Since this is no case here, it can only be that the system will decay, sometime, to a stable solution.
Or, in mathematical terms, an ideal LC (lowpass) has the transfer function:
i.e. no damping. As soon as an R comes into play (series with L):
you get the \$\zeta\$, which represents the damping. This is valid for any configuration, R represents the damping. And it makes sense, if you consider that a(n ideal) resistor is only dissipating power.