One-group analytical solutions of both direct power response and frequency response to arbitrary time-dependent reactivity oscillations are obtained. In regard to the power response, the solution can be derived from the method of singular perturbation for an arbitrary input oscillation. With the differential equations describing a source-free reactor under arbitrary reactivity changes at various time steps, it is possible to integrate the precursor balance equation through the application of prompt-jump approximation to the neutron balance equation. In regard to the frequency response, the solution is obtained by means of Fourier series expansion of arbitrary periodic input, and through the reactivity transfer function of the prompt-jump approximation. The uniqueness of these analytical solutions is that they can cover an unlimited number of oscillatory cycles with a few simple mathematical functions. These analytical solutions set down very practical groundwork with a wide spectrum of control characteristics for any reactor-kinetics code verification. Initial comparison with the K-III code calculation in fast reactor examples shows excellent results. Though the technique is demonstrated only for the one-group problem, a close form solution is difficult to come by.
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