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The general solution for a two-dimensional isotropic

Chapter 5, Problem 5.15

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QUESTION:

The general solution for a two-dimensional isotropic oscillator is given by (5.19). Show that by changing the origin of time you can cast this in the simpler form (5.20) with 6 = (Sy 6x. [Hint: A change of origin of time is a change of variables from t to t' = t to. Make this change and choose the constant to appropriately, then rename t' to be t.]

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QUESTION:

The general solution for a two-dimensional isotropic oscillator is given by (5.19). Show that by changing the origin of time you can cast this in the simpler form (5.20) with 6 = (Sy 6x. [Hint: A change of origin of time is a change of variables from t to t' = t to. Make this change and choose the constant to appropriately, then rename t' to be t.]

ANSWER:

Step 1 of 2

The displacement along x direction is  

The displacement along y direction is  

The angular speed is  

The amplitude along x direction is  

The amplitude along y direction is  

The phase along x direction is  

The phase along y direction is  

The time is t

The following equation is the general solution of 2-D isotropic oscillator is.

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