求解本征值问题 X a)+X(a)=0 X()=0X(a)=0 若入=0 微分方程的通解X(x)=A0x+B0 边界条件 A0=0,Bo=0 说明入=0时只有零解.即入=0不是本征值
Steady State Problems Forced Vibration in a String Fixed at Both Ends ¦) ¯K X00(x) + λX(x) = 0 X(0) = 0 X0 (a) = 0 ✑ eλ = 0 ©§Ï) X(x) = A0x + B0 >.^ =⇒ A0 = 0, B0 = 0 `²λ = 0k")©=λ = 0Ø´ C. S. Wu 1nù ©lCþ{()
求解本征值问题 X a)+X(a)=0 X()=0X(a)=0 当λ≠0时 微分方程通解X(x)= A sin VAx+ B cos VAx
Steady State Problems Forced Vibration in a String Fixed at Both Ends ¦) ¯K X00(x) + λX(x) = 0 X(0) = 0 X0 (a) = 0 ✑ λ 6= 0 ©§Ï) X(x) = A sin √ λx + B cos √ λx C. S. Wu 1nù ©lCþ{()
求解本征值问题 X a)+X(a)=0 X()=0X(a)=0 当λ≠0时 微分方程通解X(x)= A sin VAx+ B cos VAx 边界条件→B=04≠0c05√Aa=0
Steady State Problems Forced Vibration in a String Fixed at Both Ends ¦) ¯K X00(x) + λX(x) = 0 X(0) = 0 X0 (a) = 0 ✑ λ 6= 0 ©§Ï) X(x) = A sin √ λx + B cos √ λx >.^ =⇒ B = 0 A 6= 0 cos √ λa = 0 C. S. Wu 1nù ©lCþ{()
求解本征值问题 X a)+X(a)=0 X()=0X(a)=0 当λ≠0时,就求得 2n41\2 本征值λn 7=0,1,2,3, 2 2n+1 本征函数X(x)=sn-2nT
Steady State Problems Forced Vibration in a String Fixed at Both Ends ¦) ¯K X00(x) + λX(x) = 0 X(0) = 0 X0 (a) = 0 ✑ λ 6= 0§Ò¦ λn = 2n + 1 2a π 2 , n = 0, 1, 2, 3, · · · ¼ê Xn(x) = sin 2n + 1 2a πx. C. S. Wu 1nù ©lCþ{()
特解及一般解 方程 Yy-AnYn(=0 2n+1 20 7=0,1,2,3,… 的解为 (y)=Cn sinh 2n+1 2n+1 ny+ Dn cosh any
Steady State Problems Forced Vibration in a String Fixed at Both Ends A)9) § Y 00 n (y) − λnYn(y) = 0 λn = 2n + 1 2a π 2 , n = 0, 1, 2, 3, · · · ) Yn(y) = Cn sinh 2n + 1 2a πy + Dn cosh 2n + 1 2a πy C. S. Wu 1nù ©lCþ{()