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## Homework Statement

Q'' + 100Q' +50000Q = 4000cos(100t)

i found the general solution to be e

^{-50t}[Acos(50sqrt19)t +Bsin(50sqrt19)t]

but i have a problem with the particular solution

i tried Ce

^{i100t}

did i try the wrong expression? because when i compared coefficients, i found C=4000/40000 = 0.1

but the answer given by my lecturer is 16/170 cos100t + 4/170sin100t

idon't understand where the sin term comes from? when i try Ce

^{i100t}, i should be getting just the cosine terms right? since my target is 4000cos100t. so how come there's a sin term?

help appreciated!