Undamped Harmoni Oscillator differential equation:(adsbygoogle = window.adsbygoogle || []).push({});

mx''=-kx

(solution (to IC: x(0)=A, x'(0)=0) : x=Acos(wt) with w^{2}=k/m)

I need to find out the solution to the forced case with (Initial Condition zero):

mx''+kx=F (with F=A_{F}cos(w_{F}t) ) 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Undamped HO transfer function

**Physics Forums | Science Articles, Homework Help, Discussion**