impulse function

- anonymous

impulse function

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- anonymous

|dw:1444123497051:dw|

- anonymous

how do you write this as function?
\[X(t)=10+\delta(t)+\delta(t-1)\]

- anonymous

Im not sure. I'll show you the question

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## More answers

- anonymous

##### 1 Attachment

- 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

@dan815

- 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

an impulse has infinite height right

- 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

oh i see what ur indicating is like the area

- dan815

i think this is fine

- anonymous

so you think my function is reasonable?

- dan815

i think u shud have 10

- dan815

since 10 is not really a response

- dan815

but i dont really know, it seems like its based on convention

- dan815

i think u shudnt* have 10

- anonymous

hmm

- BAdhi

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shouldnt it be like this?? the impulse is the derivative of this graph

- dan815

then ur function would be
X(t) = 10 + integral (unit impulse) + integral 2*unitimpulse

- dan815

but they're saying sketch "response" of level vs time

- anonymous

that is a function of step functions, we can't assume that the disturbance continues after t=0 to t=1

- dan815

not level vs time right...

- dan815

|dw:1444125085374:dw|

- 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

i think its this

- dan815

the 10 isnt there anymoore in response thats initial condition

- anonymous

so its just
\[X(t)=\delta(t)+\delta(t-1)\]

- dan815

well shouldnt it be 2* impulse

- anonymous

yes sorry

- dan815

also depedns on how u drew the level graph

- anonymous

i forgot to add that in all of my equations

- dan815

u can also add an impulse of 10 at like t=-inf or something

- anonymous

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perhaps u can just scale it back by -1
and you have\[X(t)=10\delta(t)+11\delta(t-1)\]

- dan815

okay thats fine

- dan815

wait no

- dan815

its still only 2 for the 2nd one

- dan815

and 11 for hte first one

- dan815

i take it u wannna saw theres 10 in the tank and 1 added same time?

- dan815

and t=0

- 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

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

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- dan815

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- anonymous

@BAdhi we are continually removing water from the system

- dan815

just show me your step function lo... itll be so much less confusing

- anonymous

so the height will change after the impulse

- dan815

just do it depending on ur step function

- anonymous

but there is no step function...

- anonymous

lel im confused

- dan815

i thought u drew that already

- dan815

|dw:1444125831913:dw|

- 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

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

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- 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

Q(t) being the inlet flow into the tank

- dan815

again that 10 cannot be there

- dan815

having a continuous 10 means ur level was rising constant at a rate of 10 m^3 over some time increment

- anonymous

then i don't know what to do.

- 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

so this would be an instantaneous disturbance

- anonymous

does anyone understand my thought process?

- ytrewqmiswi

which topic is this question related to? :)

- anonymous

process control

- anonymous

ideas?

- anonymous

if anyone has a subscription to chegg then they have the answers, but yolo, I'm clean dry out of ideas

- anonymous

sad days

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