Applying Fourier Transform to Series RLC Circuit ODE for Capacitor Output

The discussion addresses the formulation of the ordinary differential equation (ODE) for a series RLC circuit with the output voltage across the capacitor, followed by applying the Fourier transform to determine the output response. The transfer function derived from the ODE is given as Y(ω)/X(ω) = 1 / (-LCω² + jωRC + 1), with component values R=4 Ω, L=3 H, and C=1 F, and an input spectrum X(ω)=1. It is noted that applying the Fourier transform is meaningful primarily for sinusoidal or frequency-dependent inputs rather than constant (DC) inputs. The process involves transforming the input signal, solving for the output in the frequency domain using the transfer function, and then performing an inverse Fourier transform to obtain the time-domain output y(t). References to standard textbooks and online resources for Fourier transform applications in differential equations are suggested for detailed procedural steps.
Summary generated by the language model.