Laplace transform of |sint|

[NT123]

Homework Statement

Need to find the Laplace transform of |sint| (modulus).

Homework Equations

The Attempt at a Solution

I am really not sure how to proceed here - any help would be much appreciated.

 

[Mark44]

|sin(t)| = sin(t) on [0, pi], and |sin(t)| = -sin(t) on [pi, 2pi] or on [-pi, 0]

 

[vela]

I don't know if this is the best way to go about it, but perhaps you can express the function as a convolution of a half wave with a train of delta functions (or something like that).

 

[NT123]

|sin(t)| = sin(t) on [0, pi], and |sin(t)| = -sin(t) on [pi, 2pi] or on [-pi, 0]

Thanks - I thought of this as well, but this would mean I have to integrate on each interval, and I get sum(n=0, n=inf) ((1+exp(pi*s)/exp(n*pi*s)*(s^2+1)). Is there a way to simplify this? I'm supposed to be using Laplace transforms to solve a differential equation with |sint| as the inhomogeneous part.

 

[vela]

Think geometric series where r=exp(-pi*s).

 

[NT123]

Think geometric series where r=exp(-pi*s).

Ah of course, thanks :)