Question

what is the equation for \[\large f(t) \cases{t \quad \quad 1 < t < 2 \\ 1 \quad \quad t> 2}\]
is it \[f(t) = tu(t-1) + (1-t) u(t-2)\]
or \[f(t) = u(t-1) + (1-t)u(t-2)\]
if it's worth knowing..this has something to do with heaviside functions

Answer 1

its first one i think...

Answer 2

yes that is what i think too...but in my notes there is a very ugly scratch mark, which i do not know what means

Answer 3

@sami-21 is taking a long time to type one of the two equations......

Answer 4

first one is correct
i used to remember theses like
think of them as a rectangles the height is the function the with is difference of the two ends values like for height t the width is [u(t-1)-u(t-2)
so can be written as
\[\Large =t[u(t-1)-u(t-2)+1[u(t-2)]\]
simplify
\[\Large =tu(t-1)+(1-t)u(t-2)\]
just remember
multiply the function with the difference of the unit step functions of ends points

Answer 5

yeahh..i just got confused because of my ugly handwriting. thanks =))

Answer 6

btw...for the record i do not understand what you said haha..sorry :))

Answer 7

obviously its not the 2nd one,coz for t>2,say t=4,2nd equation does not give 1..
and is that f(x) this ?

Answer 8

i just remember them because i memorize some formulas...quite ironic since im against memorization but heh. i gotta do it to survive

Answer 9

@lgbasallote i m the slowest typist search me in the guinness book :P