please show all work for parts A-C. :) Coupled Harmonic OscillatorsX, 30k3M*= x' = 2t DerivativeX= x" = 2nd DerivativekiweeA) Write down the 2nd law for each of the masses.Use coordinates x. and xz for m and M, and *, X2 and a,,a2.Hìnt : the force from spring I on m only depends on X,, but theforce from spring 2 on m depends on (x2-x1).B) To simplify, let k, = k3 =k and m= M. Rownitecquations from parrt A) right abore each other.C) Define two new variabks , X( Greek "chi") =x. +xa and AX =x-X2.Then add and subtract your two differential evahions to produce two new,but very simple (harmonic) ones.D) Write down the solution to both egvations using wo=/m, wa=ktak.and coefficients A, B,C, and D.E) Now assume k=l0k2 (this means that the two masses are "weakly coupled").Also assume x,(0) = -10cm, i,l0) =0, X. (0) =0, x1 (0) = 0. Solve forA, B,C,D, and solve for x,lt).F) Look up a trig. identity to show that your solution from part E) canbetwo differentialyourwritten in the form :x,(t) == -10cm cos ( Wotwat Cas W2-2G) For k= loN/m, m= 1.00 kg graph the behavior of x,(t) fromt=0 to t= 1TW2-WoH) Based on your answer to part W guess what x(t) looks like.Try to guess X2(t)'s functional form.

Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Coupled Harmonic Oscillators X, =0 x= x' = 2t Derivative X= x" = 2nd Derivative ki k2 k3 we M A) Write down the 2nd law for each of the masses. Use coordinates x, and x2 for m and M, and % X, and a,92.

Coupled Harmonic Oscillators X, =0 x= x' = 2t Derivative X= x" = 2nd Derivative ki k2 k3 we M A) Write down the 2nd law for each of the masses. Use coordinates x, and x2 for m and M, and % X, and a,92.

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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