Difference Between V, Vm, T, and t in Sine Wave Mathematical Expression

Dear All i hope you are good there. can any one please guide me about sine waveform mathmatical expression.
V= Vm x sin( (2xpi/T) ) x t

can any one please tell me what is a difference between V and Vm?
and T and t?

Are you sure that formula is correct? Are you sure it isn't:

V= Vm x sin( (2(pi)t/T) )

If so, then Vm is the Peak amplitude of the sinewave, and V is the amplitude at t. t can be a constant, or some function.

T is the period of the waveform.

If not, then I don't know what 't' is.

Hey Asad,

As Steve already said, Vm is the peak voltage of the signal, and t is the time elapsed since the signal generation has started. Basically, t is the independent variable that varies with time, and based on the value of t, you can calculate the voltage value of the signal.

In the case of a sine wave :

when t = 0, [(2xpi/T) * 0t] = 0 and therefore V = Vm*sin(0) = 0.
when t=T/4, [(2xpi/T) * T/4] => sin(pi/2) = 1 => V = Vm -----> This is the maximum value of the function. If you were to find the value of V at values of t, and plot them on a graph, you'd end up with a sine wave.

Hope this helps.

P.S : T is the time period, 1/T is called the frequency and (2*pi/T) is called angular frequency/

are we talking here of one-dimensional wave equation? if so, search for d'Alembert's formula.

Steve - your correction makes sense.

As t is the instantaneous time.

V is therefore a function of t.

This classic formula doesn't make much sense without it!

Asad Ali seems to have the closing bracket in the wrong place:

V= Vm x sin( (2xpi/T) ) x t

should be

V= Vm x sin( (2xpi/T) x t )