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Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple extension of this problem with three indentical masses and four identical springs. Solve for the physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two masses. We also refered to these values and vectors together as the eigen modes. I expect that we will have short discussions about the solution for the motion in each class period. mim Mi M.

Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple extension of this problem with three indentical masses and four identical springs. Solve for the physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two masses. We also refered to these values and vectors together as the eigen modes. I expect that we will have short discussions about the solution for the motion in each class period. mim Mi M.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple extension of this problem with three indentical masses and four identical springs. Solve for the physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two masses. We also refered to these values and vectors together as the eigen modes. I expect that we will have short discussions about the solution for the motion in each class period. Mi M. 个 ラX ALG 2Ya + Yb e+ Ya +2 Y% - Yc = - Yb +2 Exgenyalne eguntion g = Aje' () Y= Ae () -W? Ya -2 1 1. 2-1 Ye 2.
Transcribed Image Text:Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple extension of this problem with three indentical masses and four identical springs. Solve for the physical motion by first solving for the eigenvalues and eigenvectors as we did in lecture for two masses. We also refered to these values and vectors together as the eigen modes. I expect that we will have short discussions about the solution for the motion in each class period. Mi M. 个 ラX ALG 2Ya + Yb e+ Ya +2 Y% - Yc = - Yb +2 Exgenyalne eguntion g = Aje' () Y= Ae () -W? Ya -2 1 1. 2-1 Ye 2.
DI=0 w =+2-V2 W= -2+VE :-VZ Az Bz ALd = -2 Ya + Y -1 C2 +%+2%-Yと A -VZ Az-B2 =0 A2 + Az+ VEB2- Cz =0 - Bz +V2 C2 : 0 Bz=1 Ve (45 =2-VZ) = [ /v C2=+吉 g = Aje () V3 (4,"= +2-12) --V2 2. -VE -2 10 V, V2 0 (@-A) Na Physicd, Selutiom 4 = Ya - Y Dat Twe) Y -V2 Ya + 24, +12 (wな) Ya + Ya 12 VT Ya= 2 Ya + Ye - Ya - VZ Ya + Y + 2 Iaとと]- (w4ャ) =3% 42=0 と2-0 Ma =2A Cos (wit +4) + C Cos (Wgt + le) = 34cs(W)ナ+) w= -2+VZ +2 -VT Eagen vactors Vi•Vj =0 V: 61 V: Ai Bi
Transcribed Image Text:DI=0 w =+2-V2 W= -2+VE :-VZ Az Bz ALd = -2 Ya + Y -1 C2 +%+2%-Yと A -VZ Az-B2 =0 A2 + Az+ VEB2- Cz =0 - Bz +V2 C2 : 0 Bz=1 Ve (45 =2-VZ) = [ /v C2=+吉 g = Aje () V3 (4,"= +2-12) --V2 2. -VE -2 10 V, V2 0 (@-A) Na Physicd, Selutiom 4 = Ya - Y Dat Twe) Y -V2 Ya + 24, +12 (wな) Ya + Ya 12 VT Ya= 2 Ya + Ye - Ya - VZ Ya + Y + 2 Iaとと]- (w4ャ) =3% 42=0 と2-0 Ma =2A Cos (wit +4) + C Cos (Wgt + le) = 34cs(W)ナ+) w= -2+VZ +2 -VT Eagen vactors Vi•Vj =0 V: 61 V: Ai Bi
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