What value of s corresponds to a sinusoidal steady-state waveform?

In the context of sinusoidal steady-state analysis, the value of 's' represents a complex frequency variable that is commonly used in the Laplace transform. In this case, the correct value of 's' that corresponds to a sinusoidal steady-state waveform is expressed as jω.

The term 'j' represents the imaginary unit, and 'ω' is the angular frequency of the sinusoidal waveform. When we refer to sinusoidal steady-state conditions, we essentially mean that the system's response has stabilized and can be represented in the frequency domain using this complex frequency. This form, jω, directly aligns with the Fourier analysis where sinusoidal functions are often characterized by their frequency components.

Furthermore, the other values presented do not appropriately represent the conditions required for a sinusoidal steady-state analysis. For instance, the value of s = 0 might represent a static or DC analysis, while s = σ pertains to a real value commonly associated with exponential decay or growth rather than the oscillating nature of sinusoidal signals. The form s = σ + jω combines a real part with an imaginary part but suggests damping (due to the σ component) which is not applicable in pure sinusoidal steady states where oscillations occur without additional damping.

Thus