(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the initial value problem

y'' + 1/3y' + 4y = fk(t)

with y(0) = y'(0) = 0,

f_{k}(t) = 1/2k for 4 - k < t < 4 + k

0 otherwise

and 0 < k < 4.

(a) Write fk(t) in terms of Heaviside step functions and then solve the initial value problem.

3. The attempt at a solution

I can convert it to a heaviside function and do the laplace transform and get

f_{k}(t)= 1/2k H(t-(4-k)) - 1/2k H(t+(4-k))

and then taking the laplace transform of the entire equation get

Y(s) =^{1}/_{2k(s2+1/3 s + 4)}* (^{e-(4-k)s}/_{s}-^{e-(4+k)s}/_{s})

Im assuming this is corrent. But then how do I take the inverse laplace transform of this???

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# Homework Help: Laplace transforms of heaviside step functions

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