The Laplace transform of the function g(t) = t u(t-2) can be computed using the basic definition, L{f(t)} = ∫f(t)e^(-st)dt from 0 to infinity. By recognizing that the Heaviside step function H(t-2) is zero for t < 2, the integral simplifies to L{f(t)} = ∫2^∞ t e^(-st)dt. This approach effectively utilizes the properties of the Heaviside function to limit the bounds of integration. Additionally, the inverse Laplace transform of 1 is a relevant query, which can be addressed through established inverse transformation techniques.
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By integrating! Since H(x) is defined to be 0 for x< 0, 1 for x>= 0, H(t-2)= 0 for t< 2, 1 for t<= 2.tommyhakinen said:Homework Statement
find the laplace transform of g(t) = t u(t-2) using the basic definition.
Homework Equations
L{f(t)} = ∫f(t)e-stdt from 0 to infinity
The Attempt at a Solution
I am able to get the transform by applying the t-shifting property. However, how do I do it by using basic definition? thanks.