Normal modes-finding x1(t) & x2(t)

[gimak]

Homework Statement

https://1drv.ms/b/s!ApJAu5EMYb4JgpYy68UWlGVzp0PVLQ

Problem 21

Homework Equations

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x₁ = Ae^iw₀t + 3Be^2iw₀t
x₂ = 3Ae^iw₀t - Be^2iw₀t

The Attempt at a Solution

[/B]
At t = 0 both masses at equilibrium so the above equations simplify to:

0 = A + 3B
0 = 3A - B

Thus B = -2A. Is this wrong. Why? Here's the teacher answer: https://1drv.ms/b/s!ApJAu5EMYb4JgpYov43i3LZIO3MQhA

Why does he only work with velocity equations & not the displacement ones?

 

[mjc123]

Oh come on, this is ridiculous! Do you think it's acceptable to post a link to a document that takes 400 years to download, and just say "Problem 21" (out of 70!). Can't you be bothered to TYPE THE THING OUT? Have you read the "Guidelines for Students and Helpers"? After 40 posts you should be familiar with the etiquette. Do you expect anyone to make any effort for you if you make no effort for us?

 

[haruspex]

According to the linked solution, your "relevant equations" are not quite right. x₁ and x₂ are only the real parts of the expressions on the right. If we also allow that A and B are complex constants then the algebra in your attempt at solution only concludes that their real parts are zero. To get info on the imaginary parts you need to plug in the boundary values for velocity.