There are three particles of mass m connected to each other and to the walls by (light) springs as shown in the figure, and they oscillate in the horizontal direction. The common spring constant of the spring is k. The deviations of the first, second, and third particles from their equilibrium positions are x,y, and z, respectively. There is no air resistance and no friction. A) Write down Newton's 2nd law for each particle B) Determine the angular frequencies (frequencies) of the non-obvious normal mode solutions. C) State the eigenstates corresponding to the normal modes using the frequencies you found

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There are three particles of mass m connected to each other and to the walls by (light) springs as
shown in the figure, and they oscillate in the horizontal direction. The common spring constant of the
spring is k. The deviations of the first, second, and third particles from their equilibrium positions are
x,y, and z, respectively. There is no air resistance and no friction.
A) Write down Newton's 2nd law for each particle
B) Determine the angular frequencies (frequencies) of the non-obvious normal mode solutions.
C) State the eigenstates corresponding to the normal modes using the frequencies you found
m
m
Transcribed Image Text:There are three particles of mass m connected to each other and to the walls by (light) springs as shown in the figure, and they oscillate in the horizontal direction. The common spring constant of the spring is k. The deviations of the first, second, and third particles from their equilibrium positions are x,y, and z, respectively. There is no air resistance and no friction. A) Write down Newton's 2nd law for each particle B) Determine the angular frequencies (frequencies) of the non-obvious normal mode solutions. C) State the eigenstates corresponding to the normal modes using the frequencies you found m m
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