Integration of advanced nuclear reactors to industrial processes in an integrated energy system (IES) has many potential advantages. The coupling of nuclear power to varied industrial processes introduces additional accident scenarios unique to the specific systems included in the IES. Similarly, noise in one system of the IES could potentially create negative effects in the other systems. Because of the limited amount of comparable nuclear IES operating experience, there is added value in scoping the inherent behavior of these systems in response to these transients. This paper investigates the safety-related behavior of an open-source IES dynamic model of a fast spectrum molten salt reactor (MSR) powering a regenerative Rankine cycle for electricity production and a hybrid sulfur (HyS) cycle for hydrogen production. The simulations include a loss of cooling water to the Rankine cycle, a loss of sulfur in the HyS cycle, and the frequency characteristics of the entire IES across six orders of magnitude of frequency. The results show safe behavior in response to the two accident scenarios, wherein a disruption in heat transfer leads to increased salt temperatures and a decrease in reactor power. The frequency analysis shows that at higher frequencies, temperature changes propagating through an IES are increasingly damped to the point of negligibility.