We study how sector-specific shocks propagate in a production economy with input-output linkages and heterogeneous time to build. We show that, depending on the sector and network characteristics, one-time idiosyncratic shocks can induce a non-monotonic response of aggregate output as it converges back to steady state-a phenomenon we term 'endogenous oscillations'-and get amplified over time. We study the conditions on the network structure that generate this behavior. We introduce a measure to quantify the magnitude of such endogenous oscillations generated by a single small productivity shock. We quantify the model on US input-output data, showing that for some sectors a single shock can generate aggregate fluctuations. In particular, the magnitude of oscillations is twice as large as it would be if convergence to the steady state were always monotonic.