Laplace Transform f(t) = e^t *sin(t)sin(5t)

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SUMMARY

The Laplace Transform of the function f(t) = e^t * sin(t) * sin(5t) can be simplified using the sine addition formula. Specifically, the product sin(t) * sin(5t) can be expressed as (cos(4t) - cos(6t))/2. This transformation allows for the application of standard Laplace Transform techniques to evaluate the integral more effectively.

PREREQUISITES
  • Understanding of Laplace Transforms
  • Familiarity with trigonometric identities, specifically the sine addition formula
  • Knowledge of integral calculus
  • Basic proficiency in mathematical notation and functions
NEXT STEPS
  • Study the properties of Laplace Transforms for exponential functions
  • Learn how to apply trigonometric identities in Laplace Transform calculations
  • Explore the use of Laplace Transform tables for common functions
  • Practice solving Laplace Transforms involving products of sine functions
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Students and professionals in mathematics, engineering, and physics who are working with Laplace Transforms and need to simplify complex functions for analysis.

tim_3491
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Hey everyone

Does anyone know how to do the following Laplace Transformation

f(t) = e^t *sin(t)sin(5t)

i can do it with one sin function but don't know how to do it with 2.

any help would be appreciated.
 
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tim_3491 said:
Hey everyone

Does anyone know how to do the following Laplace Transformation

f(t) = e^t *sin(t)sin(5t)

i can do it with one sin function but don't know how to do it with 2.

any help would be appreciated.

Use the addition formula for sines:

sin(t)sin(5t) = (cos(4t) - cos(6t))/2
 

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