We demonstrate that the poly(butyl acrylate) (PBA) elastomers containing considerable amounts of dangling chains with uniform lengths exhibit pronounced viscoelastic relaxation (tan delta > 1) at characteristic frequencies. The elastomers are obtained by the copolymertization of monoacryloyl- and diacryloyl-terminated precursor PBA with narrow size distributions. The molecular weights of the precursors are smaller than the critical molecular weight for the onset of entanglement coupling. The relaxation time of the elastomers (tau(D)) is proportional to the square of the molecular weight of the dangling chains equivalent to the monofunctional PBA (M(D)), and tau(D) is about 2.5 times larger than the relaxation time of the corresponding free guest chains in the elastomers (tau(G)). These observations are close to the expectations from the Rouse-chain dynamics without entanglement effect (tau(D) similar to M(D)(2) and tau(D) = 4 tau(G)). These results provide an important basis for the understanding of the dynamics of the unentangled chains whose one end is tethered to the permanent networks. The results also offer a route of molecular control of characteristic frequency and strength of mechanical damping of elastomers.