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

解

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)

解答ステップ

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

線形 ODE を解く:

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)