Find Laplace Transform of f(t); solve IVP x'(t)-2x(t)=4f(t)

f1player

Junior Member
Joined
Feb 25, 2005
Messages
59
Consider the function f(t) = 0 when t<1 and
f(t) = t-1 when t >or equal to 1

the question reads: Find the Laplace Transform of f(t) and then solve the initial v alue problem: x'(t) -2x(t) = 4f(t), where x(0) = 0 and f(t) is given above.

The first thing i did was find the heaviside function which i got as: f(t) = x(t-1)u(t-1)
im fairly sure this is right, but how would you check this? can you somehow sub in values???

anyway, from a table this is of the form: x(t-a)u(t-a), where a=1
The laplace transform then will be of the form: e^(-as)X(s)

From this i got the laplace tranform of f(t) = e^(-s)X(s)
now, what do u do with the X(s) part? im not sure how to continue here.

For the initial value problem i get: X(s) = 4L(f(t))/(s-2), where L stands for Laplace transform.

Im stuck here, any help would be great
 
Top