This video and the interactive demo are great. I've seen various expressions of sinusoidal waves, many using different variables to represent the value of the wave, e.g. V = A sin (2πft + φ), () = (2π + φ) , and v(t)=A sin(2πft+φ) to mention a few. What do V, y(t), and v(t) represent and is there a difference when using them in this expression? Thank you!
V, y(t), and v(t) are all just a variable used to store the output of the equation, like y = 2x+4 or f(x) = 2x + 4. The variable y is often used when plotting on a graph as we're used to using an x-axis and a y-axis in mathematics. Electrical engineers often use the variable v rather than y because they're using it to represent a voltage signal. I'm an electrical engineer so that's why I'll use it frequently. The reason why you would see y(t) or v(t) is to highlight that the output variable is a function of time t (in other words the output of the equation is dependent on the variable t). This is similar to why you'll often see an equation f(x) = 2x + 4 in mathematics i.e. it highlights that the value of f is a function of x (in other words the value of f(x) depends on what the variable x is)
@@ddorran Thank you for that explanation! It makes perfect sense. I had thought it may be something to this effect but I had not been able to find a straightforward answer. I appreciate you taking the time to answer my question!
