Free Vibration in a String Fixed at Both End 寻找分离变量形式u(x,)=X(x)T()的解 a2u 0 (x)1T"(t) 0x2 T
Free Vibration in a String Fixed at Both Ends Important Remarks Separation of Variables Orthogonality: Proof Summary Conclusions Ïé©lCþ/ªu(x, t) = X(x)T(t)) ∂ 2u ∂t2 −a 2 ∂ 2u ∂x2 =0 =⇒ X00(x) X(x) = 1 a 2 T 00(t) T(t) C. S. Wu 1ù ©lCþ{()
Free Vibration in a String Fixed at Both End 寻找分离变量形式u(x,)=X(x)T()的解 a2u (x)1m"(t) 0 0x2 X( a2r(t)
Free Vibration in a String Fixed at Both Ends Important Remarks Separation of Variables Orthogonality: Proof Summary Conclusions Ïé©lCþ/ªu(x, t) = X(x)T(t)) ∂ 2u ∂t2 −a 2 ∂ 2u ∂x2 =0 =⇒ X00(x) X(x) = 1 a 2 T 00(t) T(t) =−λ C. S. Wu 1ù ©lCþ{()
Free Vibration in a String Fixed at Both End 寻找分离变量形式u(x,)=X(x)T()的解 02u 012a2=0=→ X"(x)+AX(x)=0 T"(t)+a2T(t)=0
Free Vibration in a String Fixed at Both Ends Important Remarks Separation of Variables Orthogonality: Proof Summary Conclusions Ïé©lCþ/ªu(x, t) = X(x)T(t)) ∂ 2u ∂t2 −a 2 ∂ 2u ∂x2 =0 =⇒ X00(x) + λX(x) = 0 T 00(t) + λa2T(t) = 0 C. S. Wu 1ù ©lCþ{()
Free Vibration in a String Fixed at Both End 寻找分离变量形式u(x,)=X(x)T()的解 02u 012a2=0=→ X"(x)+AX(x)=0 T"(t)+a2T(t)=0 0
Free Vibration in a String Fixed at Both Ends Important Remarks Separation of Variables Orthogonality: Proof Summary Conclusions Ïé©lCþ/ªu(x, t) = X(x)T(t)) ∂ 2u ∂t2 −a 2 ∂ 2u ∂x2 =0 =⇒ X00(x) + λX(x) = 0 T 00(t) + λa2T(t) = 0 u x=0 = 0 C. S. Wu 1ù ©lCþ{()
Free Vibration in a String Fixed at Both End 寻找分离变量形式u(x,)=X(x)T()的解 02u 012a2=0=→ X"(x)+AX(x)=0 T"(t)+a2T(t)=0 0 =→X(0)7()=0
Free Vibration in a String Fixed at Both Ends Important Remarks Separation of Variables Orthogonality: Proof Summary Conclusions Ïé©lCþ/ªu(x, t) = X(x)T(t)) ∂ 2u ∂t2 −a 2 ∂ 2u ∂x2 =0 =⇒ X00(x) + λX(x) = 0 T 00(t) + λa2T(t) = 0 u x=0 = 0 =⇒ X(0)T(t) = 0 C. S. Wu 1ù ©lCþ{()