Sin waveform equation v = Vm sin(ωt): What do t and v represent? Explanation needed

The equation v = Vm sin(ωt) describes a sinusoidal waveform where v(t) is the instantaneous voltage at time t. Vm represents the peak voltage amplitude, ω (omega) is the angular frequency defined as 2πf with f being the frequency in Hertz, and t is the instantaneous time variable in seconds. The sine wave voltage varies periodically, starting from zero, reaching positive and negative peaks within one period (T = 1/f). The waveform can be expressed as v(t) to emphasize its time dependence. A DC offset (or DC component) is a constant voltage added to the sine wave, shifting its average value away from zero; without this offset, the average value of a pure sine wave is zero. The difference between DC offset and average value is clarified: DC offset refers to the algebraic average of the waveform over a cycle, while the average value often refers to the average of the absolute values of the waveform. The RMS (root mean square) value and peak-to-peak voltage are related but distinct parameters. The discussion also explains that at typical power frequencies (50-60 Hz), the rapid voltage changes in the sine wave are too fast to be perceived visually, though at lower frequencies, modulation effects such as flickering can be observed. Additional references and explanations on waveform characteristics and definitions were provided.
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