Laplace transform of sin(4t+5)

In summary, the conversation discusses finding the Laplace transform of sin(4t+5) using a trig identity and confirming the result through direct computation.
  • #1
Mechdude
117
1

Homework Statement



get laplace transform of sin(4t+5)


Homework Equations


using some trig identity i.e. Sin(a+b)=sin(a)cos(b)+cos(a)sin(b)
or any other that could simplify it

The Attempt at a Solution


applying the trig identity
=sin(4t)cos(5)+cos(4t)sin(5)
taking the transform :
[tex] 4cos(5)\frac {1}{s^2+16} +s*sin(5)\frac{1}{s^2+16} [/tex]
why do i not trust this result, can anyone point me in the right direction?
 
Last edited:
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  • #2
Why don't you trust it? It looks fine to me.
 
  • #3
It might be right but i would like an alternative method to confirm the answer i got
 
  • #4
You could compute it directly. Integrate sin(4t+5)*exp(-st) from t=0 to t=infinity. You'll get the same thing.
 

FAQ: Laplace transform of sin(4t+5)

H2. What is the Laplace transform of sin(4t+5)?

The Laplace transform of sin(4t+5) is (4s)/(s^2+16) + (5s)/(s^2+16).

H2. What is the inverse Laplace transform of (4s)/(s^2+16) + (5s)/(s^2+16)?

The inverse Laplace transform of (4s)/(s^2+16) + (5s)/(s^2+16) is sin(4t+5).

H2. How do you apply the Laplace transform to a trigonometric function?

To apply the Laplace transform to a trigonometric function, you can use the following formula: L{sin(at+b)} = (a)/(s^2+a^2) + (b)/(s^2+a^2). This formula can be used for any trigonometric function, not just sin(4t+5).

H2. Is there a special rule for finding the Laplace transform of a shifted trigonometric function?

Yes, there is a special rule for finding the Laplace transform of a shifted trigonometric function. The formula is L{sin(at+b)} = (a)/(s^2+a^2) + (b)/(s^2+a^2). This formula can be used for any shifted trigonometric function, not just sin(4t+5).

H2. Can the Laplace transform be applied to any function?

No, the Laplace transform can only be applied to functions that satisfy certain conditions, such as being piecewise continuous and having exponential order. It is important to check the conditions before applying the Laplace transform to a function.

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