The root mean square response of a simple mechanical resonator mounted on another, which is excited by vibration of a flat motional power spectrum, is investigated theoretically for the case of no loading effect between resonators. While the solutions are not general for any pair of coupled resonators, the condition of zero loading is of particular interest, as it leads to extreme vulnerability of electronic and electromechanical equipment to shock and vibration when there is a coincidence of resonance frequencies of coupled resonators. Approximate formulas are obtained and computed by hand. The exact equation is solved on a digital computer to yield a series of curves for comparison. The approximate formulas hold surprisingly well, except when the resonators are close in frequency and highly damped. Curves of the derivative of the rms response, as one resonance frequency or the other is varied, are obtained by use of the digital computer. They illustrate the importance of mechanical tolerances in relation to detuning as a factor in design changes for improved reliability.