Hi, I'm studying transient analysis on my own and have a question about the expression or equation used when describing a shifted function. Let's say we have a simple sine wave that starts at t = 0 as shown in the first graph. We describe this as V(t) = sin(t), for instance. Now if we shift the waveform to the right so that it starts at t = 2 the expression for the function changes to V(t) = sin(t - 2) as in the second graph, and if we shift the waveform to the left so that it starts at t = -2 then the function is described as V(t) = sin(t + 2).
Why must we replace "t" with "t - 2", that is, t minus 2, if the function is to start at t equal to positive 2 and vice versa, why is the expression "t + 2", or t plus 2 used to denote that the function starts at t minus 2 seconds from the origin?
In other words the notation in the equations is counter-intuitive, yet it is correct. My question is: why is it correct, why must it be written that way?
Why must we replace "t" with "t - 2", that is, t minus 2, if the function is to start at t equal to positive 2 and vice versa, why is the expression "t + 2", or t plus 2 used to denote that the function starts at t minus 2 seconds from the origin?
In other words the notation in the equations is counter-intuitive, yet it is correct. My question is: why is it correct, why must it be written that way?
