Step function Laplace transform - can someone check my work?

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SUMMARY

The discussion centers on the Laplace transform of step functions, specifically addressing the transforms of expressions like 3u(t) - 3u(t-2) and (5t/2)u(t) - (5t/2)u(t-2). The correct Laplace transforms are derived as 3/s - 3e^{-2s}/s and 5/(2s^2) - 5e^{-2s}/(2s^2), respectively. Additionally, participants suggest using the integral definition of the Laplace transform and Euler's rule to simplify cosine factors into exponential forms for easier computation. The importance of converting phase angles to radians is also emphasized.

PREREQUISITES
  • Understanding of Laplace transforms and their properties
  • Familiarity with the unit step function, u(t)
  • Knowledge of Euler's formula for complex exponentials
  • Basic calculus, particularly integration techniques
NEXT STEPS
  • Study the integral definition of the Laplace transform
  • Learn about Euler's formula and its applications in Laplace transforms
  • Explore the properties of the unit step function in signal processing
  • Practice transforming various functions using the Laplace transform
USEFUL FOR

Students in engineering or mathematics, particularly those studying differential equations and control systems, will benefit from this discussion on Laplace transforms of step functions.

eehelp150
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Homework Statement


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Homework Equations

The Attempt at a Solution


1
##3u(t)-3u(t-2)##
##\frac{3}{s}-\frac{e^{-2s}3}{s}##

2
##\frac{5t}{2}u(t)-\frac{5t}{2}u(t-2)##
##\frac{5}{2s^2}-\frac{5e^{-2s}}{2s^2}##

3
I have no idea how to do this one.
 
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eehelp150 said:
3
I have no idea how to do this one.
How about using the (integral) definition of the Laplace transform?
You can use Euler's rule to change the cosine factor to more exponentials, leaving just exponentials in the integrand, then perhaps reverse that to get the real transform.
Don't forget to change the phase angle to radians.
 

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