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Unformatted text preview: force f ( t ) = cos(2 t ). Is there still a transient solution? Describe what happens. 1 3. Using the deﬁnition of Laplace transform, show that if L ( f ( t )) = F ( s ) , then L ( f ( t )) = sF ( s )-f (0) . 4. Solve the following ODE, using Laplace transforms: y 00 + 3 y + 3 y = u 1 ( t ) y (0) = 0 , y (0) = 0 2 5. (Extra credit) Compute the Laplace transform of a square wave - i.e., f ( t ) = +1 for t between 0 and 1, between 2 and 3, between 4 and 5, and so on, while f ( t ) =-1 for t between 1 and 2, 3 and 4, etc. (So f ( t ) is an inﬁnite series.) Try to express F ( s ) in closed form. 3...
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