## anonymous one year ago would $LT \left[ tu(t-30) \right]=\frac{ e ^{-30s} }{ s ^{2} }$ i'm not sure if applying the formula below would be right. $LT \left[ u _{c}(t)f(t-c) \right]=e ^{-cs}F(s)$

1. anonymous

we know that $LT \left[ u _{c}(t)=u(t-c) \right]=\frac{ e ^{-cs} }{ s }$

2. anonymous

just from laplace tables

3. anonymous

ideas?

4. anonymous

Have you tried going through the integration?

5. anonymous

im unsure how to do that when we are considering u(t-30)

6. anonymous

Do you know how to work with the dirac delta function?

7. anonymous

not really, we just have a table of lapalce transforms used to help us in process control. my laplace transform is limited considering we weren't taught this in engineering maths yet it has come up in a third year topic which applies laplace transforms

8. anonymous

like, i start with the integral definition, $LT(f(t)=\int\limits_{0}^{\infty}e ^{-st}tu(t-30)dt$

9. anonymous

and try integration by parts...but i'm stuck with the t*u(t-30) bit, with applying the product rule on it

10. anonymous

Ok, so if you are using integration by parts, then you are considering this integral of the from$\int\limits_{}^{}u dv = uv - \int\limits_{}^{}v du$. What are you using as your u and your dv?

11. dan815

do a change of variables

12. anonymous

dv is the exponential and u is the t*u(t-30)

13. anonymous

ohh yea neat

14. anonymous

Thanks @dan815

15. anonymous

yeah nah that drawing has confused me lel

16. dan815

lol

17. dan815

i realized using s for the different variable was bad idea lol

18. anonymous

haha no joke i was gonna say

19. dan815

now u became the variable for laplace

20. dan815

lemme think so i wonder if we gotta add some extra stuff in for this shift

21. anonymous

could we just expand those brackets

22. anonymous

so instead of s lets use 'a' as our variable

23. anonymous

(a+30)u(a)= au(a)+30u(a)

24. dan815

its best to jst graph this stuff so we know for sure we dont have anything funky going on

25. anonymous

and laplacing these would be the same...

26. anonymous

where a=t-30

27. dan815

ohh something silly here oops

28. dan815

ont need to even worry about all this apprently

29. anonymous

lel

30. dan815

this is U_c(t) by definition

31. anonymous

yep

32. anonymous

but we can't use the formula thats on the top page cause it involves f(t-c) so here c=0 for the function f, but 30 for variable 'u'

33. dan815

|dw:1443326746594:dw|

34. dan815

i think what we did might be find, think abouut it like this, what is the laplace of this bottom graph

35. dan815

fine*

36. anonymous

just a ramp function, shifted from the origin..

37. dan815

u_30(t) * ((t-30)+30)

38. dan815

with this trick now we have a new function f(t)=t+30 and f(t-c)=f(t-30)=(t-30)+30

39. dan815

yay

40. dan815

|dw:1443326992420:dw|

41. dan815

|dw:1443327070058:dw|

42. dan815

this make sense?

43. dan815

|dw:1443327188716:dw|

44. anonymous

with the first and second step |dw:1443327215719:dw|

45. dan815

ya?

46. anonymous

should the first step be f(t-30)

47. dan815

no taht is what is figven

48. dan815

so i changed it to something that is f(t-30)

49. anonymous

|dw:1443327270524:dw|

50. anonymous

like what thats mean

51. dan815

(t)

52. anonymous

oh yea ns

53. anonymous

haha

54. anonymous

yeap sweet as man, cheers!

55. dan815

ok baby

56. dan815

greetings from Canada xD

57. anonymous

ur such a lad haha

58. dan815

lel

59. anonymous

still havent moved ay

60. dan815

how r things down in australia these days

61. anonymous

yea summer is coming, soo good. only like another 2 months then i'm in 4th yr.

62. dan815

truee yeee

63. anonymous

hopefully get a job and i'll be done yesss

64. dan815

good luck :)

65. anonymous

cheers man, hbu?

66. dan815

same story pretty much, gotta do capstone next year and land jobs

67. anonymous

wuts capstone?

68. dan815

itsd like this project every engineer has to do for final year, i think u too

69. anonymous

oh like research project

70. dan815

yeah

71. anonymous

yeah that will be aids

72. dan815

yeah its just htis one course that runs for the whole year and u have to work on it in your own time

73. anonymous

yeah thats our research project haha mine will focus more on mining but not sure what yet

74. anonymous

yolo

75. dan815

oh you decided already xD i still got no idea

76. dan815

ill probably do some detection stuff i just wanna write code and make my partners do the more circuit stuff

77. anonymous

my degree is focused in minerals processing/mining so its like i am forced to do something mining like haah yeah writing code sounds fun hahaha

78. dan815

cool

79. dan815

what kind engineering is that?

80. anonymous

chemical eng. so gai

81. dan815

oooo

82. dan815

chemistry is too hard -.-

83. anonymous

haha its pretty hectic but what i enjoy so its chill as.

84. dan815

u gotta actually learn like a lot of math to do real chem, but they dont teach all that math in a chem degree

85. anonymous

too many people will fail hahaha

86. anonymous

lots of science students aren't well educated in math anyway

87. anonymous

but enough of me speaking, i need some lunch! i'll let ya know how i go with this question after. cheers mate. peace

88. dan815

alright take care!!