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jmm5872
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I am having problems understanding the "systematic method" for determining the frequencies and amplitude ratios of normal modes when a system has more than one degree of freedom. I think I initially have problems setting up the differential equation that describes the motion. Here is the problem statement:
Using either the slinky approximation or the small-oscillations approximation, find the two coupled equations of motion for the transverse displacements Ya and Yb (shown in attached picture). Use the systematic method to find the frequencies and amplitude ratios for the two normal modes.
(Description): The displacement from the relaxed position along the x-axis is given by Ya and Yb. The two normal modes are also shown but I don't think I needed to draw them. !FORGOT TO MENTION...they masses are attached to springs!
So my initial problem is my confusion in setting up the two coupled equations of motion. (They are set up so that gravity does not affect the motion). Here is what I assumed for the two equations:
MYa" = -TYa + T(Yb - Ya)
MYb" = -T(Yb - Yb) - TYb
Let me first see if this is even correct before I move on.
Using either the slinky approximation or the small-oscillations approximation, find the two coupled equations of motion for the transverse displacements Ya and Yb (shown in attached picture). Use the systematic method to find the frequencies and amplitude ratios for the two normal modes.
(Description): The displacement from the relaxed position along the x-axis is given by Ya and Yb. The two normal modes are also shown but I don't think I needed to draw them. !FORGOT TO MENTION...they masses are attached to springs!
So my initial problem is my confusion in setting up the two coupled equations of motion. (They are set up so that gravity does not affect the motion). Here is what I assumed for the two equations:
MYa" = -TYa + T(Yb - Ya)
MYb" = -T(Yb - Yb) - TYb
Let me first see if this is even correct before I move on.
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