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| − | = Homework 8 Collaboration Area = | + | == Homework 8 Collaboration Area == |
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| + | Question on problem 15 in Sec 6.6. | ||
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| + | I tried to obtain the expression for | ||
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| + | s/(s + 1) * 1/(s+1) | ||
| + | |||
| + | but am not getting the correct result in the Laplace table of | ||
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| + | t sin t. | ||
| + | |||
| + | I am using the convolution of | ||
| + | cos(tau)*sin(t-tau). There is no t term in sight. Is it okay to read off the | ||
| + | table? Even if it is, shouldn't the result be the same? | ||
| + | |||
| + | Answer: | ||
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| + | To find the inverse Laplace transform of | ||
| + | |||
| + | s/(s + 1) * 1/(s+1) | ||
| + | |||
| + | you'll need to compute the convolution integral: | ||
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| + | <math>\int_0^t \cos(\tau)\sin(t-\tau)\ d\tau.</math> | ||
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| + | You'll have to use a formula for the sine of the | ||
| + | difference of two angles and be very careful. | ||
| + | Remember, t acts like a constant in the integrals. | ||
| + | |||
| + | There is only one correct answer, so you should get | ||
| + | it that way. (If it looks different than the back | ||
| + | of the book, a trig identity might be at fault.) | ||
| + | |||
| + | [[2010 MA 527 Bell|Back to the MA 527 start page]] | ||
| + | |||
| + | [[Course List|To Rhea Course List]] | ||
| + | |||
| + | [[Category:MA5272010Bell]] | ||
Revision as of 08:38, 18 October 2010
Homework 8 Collaboration Area
Question on problem 15 in Sec 6.6.
I tried to obtain the expression for
s/(s + 1) * 1/(s+1)
but am not getting the correct result in the Laplace table of
t sin t.
I am using the convolution of cos(tau)*sin(t-tau). There is no t term in sight. Is it okay to read off the table? Even if it is, shouldn't the result be the same?
Answer:
To find the inverse Laplace transform of
s/(s + 1) * 1/(s+1)
you'll need to compute the convolution integral:
$ \int_0^t \cos(\tau)\sin(t-\tau)\ d\tau. $
You'll have to use a formula for the sine of the difference of two angles and be very careful. Remember, t acts like a constant in the integrals.
There is only one correct answer, so you should get it that way. (If it looks different than the back of the book, a trig identity might be at fault.)
