What is the difference between mode ratio and mode shape?

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The discussion clarifies the distinction between mode ratio and mode shape in the context of mechanical vibrations. A mode ratio refers to the ratio of two coordinates at natural frequency when only two coordinates are involved. In contrast, a mode shape is defined when more than two coordinates are used to describe the mode vector. Understanding these terms is essential for solving problems related to vibrations in mechanical systems. The explanation highlights the importance of recognizing the number of coordinates involved in determining the appropriate terminology.
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This isn't a homework question in its entirety, I'm just wondering what the difference is between a Mode ratio and a mode shape? I'm taking a mechanical vibrations course and trying to figure out what the problem is asking for when it wants a mode shape...
 
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If the problem involves only two coordinates, then the ratio of those two coordinates at the natural frequency is the mode ratio (as I recall). If there are more than two coordinates involved to define the mode vector, this is called the mode shape.
 

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