- #1
danj303
- 15
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Homework Statement
Consider the initial value problem
y'' + 1/3y' + 4y = fk(t)
with y(0) = y'(0) = 0,
fk(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.
The Attempt at a Solution
I can convert it to a heaviside function and do the laplace transform and get
fk(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?