Re: [理工] [工數]-微分方程
※ 引述《CRS339 (機車)》之銘言：
: d^2x/dt^2 + 4x =2cos3t + 3sin3t ; x=3 and dx/dt=2 for t=0
: 還請幫解惑 指點指點
: 謝謝
兩端取 Laplace轉換可得
2 2s 9
s X -3s -2 + 4X = --------- + ---------
s^2 + 9 s^2 + 9
2 2s + 9
=> (s + 4)X = -------- + (3s + 2)
s^2 + 9
2s + 9 3s + 2
=> X = -------------------- + ---------
(s^2 + 4)(s^2 + 9) s^2 + 4
1/5(2s + 9) -1/5(2s + 9) 3s + 2
= ------------- + -------------- + ---------
s^2 + 4 s^2 + 9 s^2 + 4
(17/5)s + 19/5 (-2/5)s + (-9/5)
= --------------- + ------------------
s^2 + 4 s^2 + 9
取反轉換可得
17 19 2 3
x(t) = [ ----cos2t + ----sin2t - ---cos3t - ---sin3t ]u(t)
5 10 5 5
現在流行+u(t)是吧
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