Moving Blocks

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Even if A and B do not execute SHM, path of P will be the same - an ellipse.

The mechanism is called an Elliptical Trammel. Every point on arm ABP traces an ellipse, with some special cases like the midpoint M of AB tracing a circle (ellipse with equal axes) and points A and B tracing double lines (which are ellipses with one axis of zero length).

Anyway, to find locus of P -

Let $\theta$ = angle AB makes with x axis

Then, $P_{x} = b \cos \theta$ and $P_{y} = a \sin \theta$ . . . . parametric equation of ellipse

This is called the trammel of Archimedes, but devices that draw conic sections were more likely to be invented during the Roman Era (with the exception of the compass).

Well...I too cud see in the gif...that it was an ellipse.....but its imp to know the concept used!!!

There is no difficulty in solving this just a simple mind work ,creativity ,and. Visualization would suffice to do this.As the rod moves it attains its maximum displacement when one Block comes to mean position and whn the other block comes to mean position it comes near to the block . there are only two possibilities circle or ellipse ...as it is not having a same radius it is ELLIPSE......

just close the box with something such that you can see only the tip of the rod. You will find it

Symmetrical about x and y with two far and two near. Initially I thought it could be a circle but I felt quite strange that a circle does not seem to be complicated. Then I checked that cardioid is non symmetrical about x and y. If this can draw out a rectangle, then this is too surprising. Only then I noticed the difference of long and short. As an ellipse matches best, I selected ellipse. To be more precise, we must write its equations. I applied a logic of negation instead of confirmation.