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 Cei100t
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 Cei100t, i should be getting just the cosine terms right? since my target is 4000cos100t. so how come there's a sin term?