## anonymous one year ago impulse function

1. anonymous

|dw:1444123497051:dw|

2. anonymous

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

3. anonymous

Im not sure. I'll show you the question

4. anonymous

5. 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

6. anonymous

@dan815

7. 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)

8. dan815

an impulse has infinite height right

9. 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

10. dan815

oh i see what ur indicating is like the area

11. dan815

i think this is fine

12. anonymous

so you think my function is reasonable?

13. dan815

i think u shud have 10

14. dan815

since 10 is not really a response

15. dan815

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

16. dan815

i think u shudnt* have 10

17. anonymous

hmm

|dw:1444124866547:dw| shouldnt it be like this?? the impulse is the derivative of this graph

19. dan815

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

20. dan815

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

21. anonymous

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

22. dan815

not level vs time right...

23. dan815

|dw:1444125085374:dw|

24. 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

25. dan815

i think its this

26. dan815

the 10 isnt there anymoore in response thats initial condition

27. anonymous

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

28. dan815

well shouldnt it be 2* impulse

29. anonymous

yes sorry

30. dan815

also depedns on how u drew the level graph

31. anonymous

i forgot to add that in all of my equations

32. dan815

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

33. anonymous

|dw:1444125308190:dw| perhaps u can just scale it back by -1 and you have$X(t)=10\delta(t)+11\delta(t-1)$

34. dan815

okay thats fine

35. dan815

wait no

36. dan815

its still only 2 for the 2nd one

37. dan815

and 11 for hte first one

38. dan815

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

39. dan815

and t=0

40. anonymous

im not following, why is it 2, when we are inputting an impulse of a factor of 1 greater than the first impulse?

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

42. anonymous

43. dan815

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44. anonymous

@BAdhi we are continually removing water from the system

45. dan815

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

46. anonymous

so the height will change after the impulse

47. dan815

just do it depending on ur step function

48. anonymous

but there is no step function...

49. anonymous

lel im confused

50. dan815

i thought u drew that already

51. dan815

|dw:1444125831913:dw|

52. 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..

53. 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

54. anonymous

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55. 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)=??

56. anonymous

Q(t) being the inlet flow into the tank

57. dan815

again that 10 cannot be there

58. dan815

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

59. anonymous

then i don't know what to do.

60. 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.

61. anonymous

so this would be an instantaneous disturbance

62. anonymous

does anyone understand my thought process?

63. ytrewqmiswi

which topic is this question related to? :)

64. anonymous

process control

65. anonymous

ideas?

66. anonymous

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

67. anonymous