Laplace Transform. Is this correct?

Click For Summary
SUMMARY

The Laplace Transform of the function ƒ(t) = 1.15t is correctly calculated as L(f(t)) = 1 / (s - ln(1.15)). This conclusion is based on the standard Laplace Transform table, which provides the necessary equations for transforming time-domain functions into the s-domain. The use of the natural logarithm of the coefficient 1.15 is essential in deriving the correct transform.

PREREQUISITES
  • Understanding of Laplace Transforms and their applications
  • Familiarity with the standard Laplace Transform table
  • Basic knowledge of natural logarithms
  • Ability to manipulate algebraic expressions involving functions of time
NEXT STEPS
  • Study the properties of Laplace Transforms for linearity and time-shifting
  • Explore inverse Laplace Transform techniques for recovering time-domain functions
  • Learn about the application of Laplace Transforms in solving differential equations
  • Investigate the use of Laplace Transforms in control systems analysis
USEFUL FOR

Students studying engineering mathematics, professionals in control engineering, and anyone interested in applying Laplace Transforms to solve differential equations.

avion105
Messages
2
Reaction score
0

Homework Statement



ƒ(t) = 1.15t


Homework Equations



Standard Laplace Transform Table

The Attempt at a Solution



L(f(t)) = e(t * ln(1.15) = 1 / (s - ln(1.15))
 
Physics news on Phys.org
Yes, that is correct.
 

Similar threads

What is the Inverse Laplace Transform of e^(-sx^2/2)?
  • · Replies 10 ·
Replies
10
Views
3K
Laplace transform of cosine squared function
  • · Replies 1 ·
Replies
1
Views
1K
Does the Laplace Transform of e^(at)/t Exist?
  • · Replies 4 ·
Replies
4
Views
3K
Laplace transforms for which value of s?
  • · Replies 2 ·
Replies
2
Views
2K
Mellin transform of Dirac delta function ##\delta(t-a)##
  • · Replies 3 ·
Replies
3
Views
3K
Determine limits of integration in double integral change of variables
  • · Replies 2 ·
Replies
2
Views
2K
Finding the Laplace transform of a piecewise function
  • · Replies 3 ·
Replies
3
Views
2K
Laplace transform of an ODE with a non-smooth forcing function
  • · Replies 2 ·
Replies
2
Views
2K
A tricky inverse Laplace transform
  • · Replies 8 ·
Replies
8
Views
3K
Laplace transform applied to a differential equation
  • · Replies 1 ·
Replies
1
Views
1K