What is the Laplace Transform of |sint|?

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SUMMARY

The Laplace transform of |sin(t)| can be determined by considering its behavior over specific intervals. On the interval [0, π], |sin(t)| equals sin(t), while on [π, 2π] and [-π, 0], it equals -sin(t). The solution involves integrating over these intervals and utilizing the properties of geometric series, specifically with r = exp(-πs). The final expression for the Laplace transform incorporates a summation that simplifies the calculation.

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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.
 
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|sin(t)| = sin(t) on [0, pi], and |sin(t)| = -sin(t) on [pi, 2pi] or on [-pi, 0]
 
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).
 
Mark44 said:
|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.
 
Think geometric series where r=exp(-pi*s).
 
vela said:
Think geometric series where r=exp(-pi*s).
Ah of course, thanks :)
 

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