A voltage E1(t)=(2+t^2)u(t+2) is passed through a delay line of 6 sec.Write one expression for the output voltage E2(t).

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A voltage E1(t)=(2+t^2)u(t+2) is passed through a delay line of 6 sec.Write one expression for the output voltage E2(t).

Mathematics
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whts a delay line do??
u(t+2) means the voltage started at t=-2 seconds , now if we were to delay it 6seconds, that would mean that the voltage would start at t=4seconds
however , we want the same value of the voltage to be obversed at that time, it is note merely enough to just change our unit step function , we need to change the actual function itself

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see the first voltage, it started at t=-2 , and it had a value of 6V , now for us to delay the voltage by 6 seconds means that the still want the same initial voltage and same rate of increase in voltage , just with everything shifted.
so we must change the voltage to v(t) =\[(2+(t-6)^2)u(t-4)V\]

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