FAQ
TL;DR: To model AC signals, use ωt as phase; “w stands for the angular frequency in radians per second.” There are 2π radians per cycle. Convert units consistently to analyze, synthesize, and plot one clean 20 ms cycle for 50 Hz signals. [Elektroda, Steve Lawson, post #21664580]
Why it matters: This FAQ helps students and engineers avoid unit mix-ups when building and plotting sinusoidal waveforms.
Quick Facts
- 1 radian = 57.2957795 degrees; keep units consistent across your equation and plots. [Elektroda, Steve Lawson, post #21664573]
- There are 2π radians per cycle; ω relates to f by a 2π factor. [Elektroda, Steve Lawson, post #21664580]
- A 50 Hz mains cycle lasts 20 ms; plotting one cycle shows the entire repeating shape. [Elektroda, Earl Albin, post #21664579]
- Example conversions: 40° ≈ 0.698 rad; 15° ≈ 0.262 rad for phase terms. [Elektroda, Rick Rude, post #21664574]
- You can plot voltage vs radians directly or convert ωt to degrees first. [Elektroda, Steve Lawson, post #21664575]
What does wt mean in a sine like v(t) = A·sin(ωt + φ)?
wt is the instantaneous phase from angular frequency ω (radians/second) multiplied by time t. That product gives the angle used by the sine. As Steve explains, frequency f (cycles/second) is distinct from angular frequency. Quote: “w stands for the angular frequency in radians per second.” [Elektroda, Steve Lawson, post #21664580]
How do I convert between degrees and radians for phase?
Use radians = degrees × π/180 and degrees = radians × 180/π. Keep the same unit across ωt and any constant phase φ before evaluating sin(). A common check: 1 radian ≈ 57.2957795°. [Elektroda, Steve Lawson, post #21664573]
How do I handle phase offsets like +40° or −15°?
Convert the offsets to radians if ωt is in radians, or convert ωt to degrees if you prefer degrees. Example conversions shown: 40° ≈ 0.6981 rad and 15° ≈ 0.2617 rad. Apply the sign to φ inside sin(ωt + φ). [Elektroda, Rick Rude, post #21664574]
Is ω the same as frequency f?
No. Frequency f measures cycles per second, while ω is angular frequency in radians per second. They are related by ω = 2πf because each cycle spans 2π radians. Mixing them causes a 2π scale error. [Elektroda, Steve Lawson, post #21664580]
How long is one 50 Hz cycle and why plot only one?
One 50 Hz cycle is 1/50 s = 20 ms. Plotting one cycle is enough because the waveform repeats each cycle. Set your time axis from 0 to 20 ms to capture a full period cleanly. [Elektroda, Earl Albin, post #21664579]
What’s a simple 3‑step way to plot a phased sine in Excel?
- Create a time column from 0 to 20 ms in 50 steps of 0.4 ms.
- Compute the argument column as ωt ± phase, keeping consistent units.
- Compute A·sin(argument) and chart argument (x) vs result (y). [Elektroda, Earl Albin, post #21664577]
Do I need to plot 0–360° or 0–2π?
Either works, but keep it consistent. You can plot voltage versus radians directly, or convert the ωt terms to degrees first. Do not mix units within the same equation or chart. [Elektroda, Steve Lawson, post #21664575]
What does the “Vol” term in some equations mean?
In the thread, “Vol” appears ambiguous. Treat it as incorrect in that form and proceed without it, documenting why you removed it. Use a clear amplitude A instead. [Elektroda, Earl Albin, post #21664577]
How should I choose the sampling step for plotting?
Use a small, regular step that divides the period cleanly. Example: for 50 Hz, 0.4 ms steps yield 50 samples per 20 ms cycle, producing a smooth plot and simple math. [Elektroda, Earl Albin, post #21664579]
What’s a common mistake that breaks the waveform?
Confusing frequency f with angular frequency ω. Using f inside sin() without converting to ω under-scales the phase by 2π and distorts timing. “It’s important to distinguish frequency and angular frequency.” [Elektroda, Steve Lawson, post #21664580]
How do I compute phase at a specific time t?
Multiply angular frequency by time, then add any phase offset: θ(t) = ωt + φ. Evaluate sin(θ) using the same angle unit throughout. This directly yields the instantaneous voltage when scaled by amplitude A. [Elektroda, Steve Lawson, post #21664580]
Should sin() use degrees or radians in my calculator or code?
Use whichever your tool expects, but match your inputs. Either convert constants to radians and keep ωt in radians, or convert ωt to degrees. Consistency prevents phase errors and misaligned plots. [Elektroda, Steve Lawson, post #21664571]
