What is the issue with applying the Laplace transform to tcos(4t)?

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Homework Help Overview

The discussion revolves around the application of the Laplace transform to the function f(t) = tcos(4t). Participants are examining the formula for the Laplace transform of t multiplied by a function and the resulting signs in their calculations.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to apply the formula t^n f(t) = (-1)^n d^nF(s)/ds^n and are questioning the signs in their results. There are discussions about the correctness of derivatives and the application of the quotient rule.

Discussion Status

There is an ongoing exploration of the signs in the results obtained from applying the Laplace transform formula. Some participants are clarifying their understanding of the derivative calculations, while others express confusion about the signs and the correctness of their approaches.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can share or the methods they can use. There is a noted discrepancy in the application of the formula and the resulting expressions.

Feodalherren
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Homework Statement


f(t)=tcos(4t)

Homework Equations



tnf(t)=(-1)n dF(s)/dsn

The Attempt at a Solution


I don't understand why this formula is giving me the oppiste sign of the answer.

If I apply the formula I get

(16-s2)/(s2+16)2

Because n=1 I need to multiply by a negative but this yields the incorrect answer.
 
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Yours looks different than the one we use. Try it as:
qdZ4Kvq.jpg
 
Feodalherren said:

Homework Statement


f(t)=tcos(4t)

Homework Equations



tnf(t)=(-1)n dF(s)/dsn

The Attempt at a Solution


I don't understand why this formula is giving me the oppiste sign of the answer.

If I apply the formula I get

(16-s2)/(s2+16)2

Because n=1 I need to multiply by a negative but this yields the incorrect answer.

$$-\frac{-s^2+16}{(s^2+16)^2}=\frac{s^2-16}{(s^2+16)^2}$$which is correct.
 
His answer doesn't have a negative in front?
Edit: nevermind, looking at wrong thing. Carry on
 
But that's not what I'm getting.

Taking the derivative of s/(s2+16)

= (s(2s)-(s2+16)/(s2+16)2

now multiply the result with -1 and we get the opposite sign for the answer.
 
Feodalherren said:
But that's not what I'm getting.

Taking the derivative of s/(s2+16)

= (s(2s)-(s2+16)/(s2+16)2

now multiply the result with -1 and we get the opposite sign for the answer.

That is because your quotient rule is wrong.
 
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Likes   Reactions: Feodalherren
Ah I see. Thank you!
 

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