## anonymous one year ago unit step function. #dan815

1. anonymous

|dw:1443667583385:dw|

2. anonymous

just to be clear, we can represent this as X(t)=u(t)+2u(t-1)

3. dan815

you can rewrite that as a summation of some other step functions

4. dan815

yes

5. anonymous

SIK

6. dan815

uhh lemem see

7. anonymous

getting the hang of this

8. anonymous

actual problem is this sox

9. dan815

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10. dan815

yeah what u want to do is actually u(t) + u(t-1)

11. anonymous

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12. anonymous

X(t)=11u(t)+12u(t-1)

13. dan815

the graph is a bit confusing u want it 10 until 0?

14. anonymous

10

15. dan815

what u did will result in 23 at your highest step

16. anonymous

has constant feed rate of 10m^3/min (theoretically) but at time t=0, a disturbance pushes 1m^3 of water into the tank and an extra 2m^3 of water at t=1min (So an additional 1m^3 of water per min)

17. dan815

okay lemme get this right though u want 10 before 0?

18. dan815

u know for laplace transform it cuts off the part before 0

19. dan815

because if u look at the power series summation n from 0 to inf x^n this only converges when x<1

20. dan815

|X|<1

21. anonymous

yea, they draw these graphs just to show use the theoretical flow regime. yes it cuts off at 0 for laplacing, but we have questions that show graphs like these.

22. anonymous

because another example, where

23. dan815

okay okay lemme make sure about 1 more thing

24. dan815

upto where do u want the 10 on the negative side

25. dan815

forever?

26. anonymous

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27. anonymous

they have function X(t)=90(u(t)-u(t-0.1))

28. anonymous

so pretty much i just applied it to get X(t)=11u(t)+12u(t-1) but need confirmation

29. dan815

whats the question again

30. anonymous

|dw:1443668159355:dw|

31. dan815

11u(t)+12u(t-1) that wont give u that

32. anonymous

i just need to find this function as step function

33. anonymous

so i can solve this silly problem

34. dan815

lol okay ill show u best way to do this

35. dan815

just draw some step functions and see how to add them

36. anonymous

neeeed

37. anonymous

38. anonymous

question is this btw for anyones interest

39. anonymous

40. anonymous

41. dan815

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42. anonymous

10+u(t)+u(t-1)?

43. dan815

ya that works

44. anonymous

say we have this drawing again

45. anonymous

|dw:1443668443342:dw|

46. dan815

yep

47. anonymous

they said the step function was x(t)=90(u(t)-u(t-0.1))

48. dan815

that doesnt work

49. anonymous

50. dan815

they are missing a 10

51. dan815

plug in a value for t lets say t=2

52. anonymous

53. anonymous

it legit has it in a book haha , omg I'm confused

54. dan815

maybe they just dont want to cover the 10, what they have there is

55. dan815

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56. anonymous

perhaps they just shift it down so its just normalises it

57. anonymous

which really would affect the problem aye

58. anonymous

wouldn't*

59. anonymous

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60. anonymous

would be X(s)=10u(t)+11u(t-1)

61. dan815

X(s)=10*U(t)+u(t-1)

62. anonymous

why isn't it 11u(t-1)? aren't we increasing an addition m^3 after t=1min

63. anonymous

ohhhhhhh

64. anonymous

pellet

65. dan815

lolq

66. anonymous

67. dan815

yes

68. anonymous

and u just add a step function of magnitude 1 extra YRESSSSDQIDLFYHQBLERBFHIRL

69. anonymous

DAN u da man

70. dan815

i beeen telling u this lool

71. anonymous

shhhhhhhhh

72. anonymous

hahahahahaa

73. anonymous

3weeks of lapalce transforms and its a subject inside this course, i rekn I'm doing well to grasp a lot of things haha

74. anonymous

that just clicked aye

75. anonymous

nigsss

76. dan815

lol!

77. dan815

i think laplace transforms might be a waste of time

78. dan815

who knows

79. dan815

its to introduce u to fourier transforms

80. anonymous

lel, we use lapalce transforms in process control so its easier to solve differential equations (approximate it using linearisation)

81. dan815

ye but eventually DE become too hard with laplace, so u gotta use fourier transforms for PDES

82. dan815

i better get back to work T_T

83. anonymous

yeah tru dat but that was for eng math. i guess we aren't looking at too hard of ODE's but i guess they teach us this smack and we have to learn their way of calculating there questions

84. anonymous

yea np, peace