q^{''}+2q^'+1/(0.25)q=50cos(sqrt(3)t)

解答

q^{^{''}} + 2 q^{^{'}} + \frac{1}{0.25} q = 50 cos (3 t)

q (t) = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{100 3}{13} sin (3 t) + \frac{50}{13} cos (3 t)

求解步骤

q^{''} (t) + 2 q^{'} (t) + \frac{1}{0.25} q (t) = 50 cos (3 t)

求解线性方程:

q (t) = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{100 3}{13} sin (3 t) + \frac{50}{13} cos (3 t)

q (t) = e^{- t} (c_{1} cos (3 t) + c_{2} sin (3 t)) + \frac{100 3}{13} sin (3 t) + \frac{50}{13} cos (3 t)

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