Undamped Harmoni Oscillator differential equation: mx''=-kx (solution (to IC: x(0)=A, x'(0)=0) : x=Acos(wt) with w2=k/m) I need to find out the solution to the forced case with (Initial Condition zero): mx''+kx=F (with F=AFcos(wFt) ) evaluating with the transfer function. But I m not sure this transfer function does exists, or is limied. Second question) Is the solution to the Undamped HO forced sinusoidally stable ? I suppose not, because without energy dissipation, the energy that enter is never consumed and just adds up to the system. But I m not sure, I have not time to calculate the solution which i haven't found. Third ) In case of damped HO forced with a sinusoid, in the resonant band of frequencies, where there is amplification, the response function is higher than the input forcing sinusoid. Is a way to see the mathematic of energy transfer from input to output ? There is no creation of energy in the system , just the amplitude of the oscillation of the input is amplified, but this doesn't mean that the power of the output is higher than the input. Isn't it?