We use low-degree p-mode data, collected in integrated sunlight by the Birmingham Solar-Oscillations Network (BiSON), to derive the distribution of the observed strengths of the solar oscillations. We demonstrate that certain features of the observations cannot be explained by a model of the oscillations that is based upon a stochastically forced, damped harmonic oscillator. The solution of the equation of motion of the oscillator, as derived by the use of the Laplace transform, is presented, and its application to the simulation of real p-mode data, in the form of a coded algorithm, is discussed. A variety of tests are applied - both in the time and in the frequency domains - to artificially generated time series. These confirm that the model serves both as a useful diagnostic tool and for providing additional insight into the p-mode excitation and damping problem.