anonymous
  • anonymous
impulse function
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1444123497051:dw|
anonymous
  • anonymous
how do you write this as function? \[X(t)=10+\delta(t)+\delta(t-1)\]
anonymous
  • anonymous
Im not sure. I'll show you the question

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anonymous
  • anonymous
anonymous
  • anonymous
i don't think its saying that the 1ft^3 of water still happen from t=0min to t=1 mins, otherwise it would be a step function (not an impulse function). Im not entirely sure
anonymous
  • anonymous
@dan815
anonymous
  • anonymous
because in the end, after the last impulse, you want the inlet to be running at 10ft^3 of water (Since that is its steady state value; the impulses come from disturbances)
dan815
  • dan815
an impulse has infinite height right
anonymous
  • anonymous
yes, but i guess we say that an impulse of 2 is greater than an impulse of 1, hypothetically speaking, despite both having infinite height
dan815
  • dan815
oh i see what ur indicating is like the area
dan815
  • dan815
i think this is fine
anonymous
  • anonymous
so you think my function is reasonable?
dan815
  • dan815
i think u shud have 10
dan815
  • dan815
since 10 is not really a response
dan815
  • dan815
but i dont really know, it seems like its based on convention
dan815
  • dan815
i think u shudnt* have 10
anonymous
  • anonymous
hmm
BAdhi
  • BAdhi
|dw:1444124866547:dw| shouldnt it be like this?? the impulse is the derivative of this graph
dan815
  • dan815
then ur function would be X(t) = 10 + integral (unit impulse) + integral 2*unitimpulse
dan815
  • dan815
but they're saying sketch "response" of level vs time
anonymous
  • anonymous
that is a function of step functions, we can't assume that the disturbance continues after t=0 to t=1
dan815
  • dan815
not level vs time right...
dan815
  • dan815
|dw:1444125085374:dw|
anonymous
  • anonymous
i have the level v time sorted once i find the solution to the initial flow rate. i can just apply laplace and first order principles. but this is the important bit
dan815
  • dan815
i think its this
dan815
  • dan815
the 10 isnt there anymoore in response thats initial condition
anonymous
  • anonymous
so its just \[X(t)=\delta(t)+\delta(t-1)\]
dan815
  • dan815
well shouldnt it be 2* impulse
anonymous
  • anonymous
yes sorry
dan815
  • dan815
also depedns on how u drew the level graph
anonymous
  • anonymous
i forgot to add that in all of my equations
dan815
  • dan815
u can also add an impulse of 10 at like t=-inf or something
anonymous
  • anonymous
|dw:1444125308190:dw| perhaps u can just scale it back by -1 and you have\[X(t)=10\delta(t)+11\delta(t-1)\]
dan815
  • dan815
okay thats fine
dan815
  • dan815
wait no
dan815
  • dan815
its still only 2 for the 2nd one
dan815
  • dan815
and 11 for hte first one
dan815
  • dan815
i take it u wannna saw theres 10 in the tank and 1 added same time?
dan815
  • dan815
and t=0
anonymous
  • anonymous
im not following, why is it 2, when we are inputting an impulse of a factor of 1 greater than the first impulse?
BAdhi
  • BAdhi
idont know why we need laplace transform and stuff since it jst ask to draw the level of the tank .. and from my graph we can easily find the levels at t=.5, 1, 1.5
anonymous
  • anonymous
dan815
  • dan815
|dw:1444125541664:dw|
anonymous
  • anonymous
@BAdhi we are continually removing water from the system
dan815
  • dan815
just show me your step function lo... itll be so much less confusing
anonymous
  • anonymous
so the height will change after the impulse
dan815
  • dan815
just do it depending on ur step function
anonymous
  • anonymous
but there is no step function...
anonymous
  • anonymous
lel im confused
dan815
  • dan815
i thought u drew that already
dan815
  • dan815
|dw:1444125831913:dw|
anonymous
  • anonymous
well its kinds ambiguous to me cause you aren't adding water from the first disturbance from t=0 to t=1, only instantaneously..
anonymous
  • anonymous
like all it is, is just a spike to the inflow, and thats it. it isn't flowing 11ft^3 of water from t=0 to t=1. only at an instantaneous period
anonymous
  • anonymous
|dw:1444126223534:dw|
anonymous
  • anonymous
any thoughts? i just need to find the function of inflow and i will be set. i just need to find what Q(t)=??
anonymous
  • anonymous
Q(t) being the inlet flow into the tank
dan815
  • dan815
again that 10 cannot be there
dan815
  • dan815
having a continuous 10 means ur level was rising constant at a rate of 10 m^3 over some time increment
anonymous
  • anonymous
then i don't know what to do.
anonymous
  • anonymous
because, we aren't really adding step functions, because it would have told us that from t=0 to t=1, 1ft^3 is being added to the tank, (that is a step function) but here it doesn't say.
anonymous
  • anonymous
so this would be an instantaneous disturbance
anonymous
  • anonymous
does anyone understand my thought process?
ytrewqmiswi
  • ytrewqmiswi
which topic is this question related to? :)
anonymous
  • anonymous
process control
anonymous
  • anonymous
ideas?
anonymous
  • anonymous
if anyone has a subscription to chegg then they have the answers, but yolo, I'm clean dry out of ideas
anonymous
  • anonymous
sad days

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