Given the piecewise continuous funtion

Question

{ e^3t, 0≤t<1

f(t)= {t-1, 1≤t‹2

{ 1, t≥2

Express f(t)) in terms step function and find L{f(t)}

Answer 1

The step function corresponding to the function defined is:

f(t) = e^3t + (-e^3t+t-1)u(t-1) + (-t+2)u(t-2)

The Laplace Transform is

L(e^3t) + e^-sL(e^3(t+1)+t) + e^-2sL(-t) where L is the Laplace transform

The formula used to deal with unit step function was L(u(t-τ)f(t)) = e^-sτL(f(t+τ))

Using tables for transform...

1/(s-3) + e^-s(e³/(s-3) + 1/s²) + e^-2s(-1/s²)

Please go over my math as this calculation is fidgety.

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