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Suppose we have such construction as shown at the picture. The vertical frame starts from rest with constant acceleration $a.$ Find final angle $\theta,$ assuming no friction. Also plot $\dot\theta$ as function of $\theta.$

From Newton second law i have that $ma_{collar} = N\sin\theta = mg\cos\theta\sin\theta = \frac{1}{2}mg\sin{2\theta}.$ From this i can find $\theta_{maximum}.$ But i still need to plot the graph, i think i need to build some differential equation for it.

enter image description here

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    $\begingroup$ I don't think you need to build a full differential equation: draw the forces on the mass and the relationship will follow because it's asking for $\dot\theta(\theta)$ and not $\dot\theta(t)$. I suppose you are allowed to neglect the moment of inertia of A - although it is clearly rotating about the axis perpendicular to the page and is of finite size as drawn... $\endgroup$
    – Floris
    Jan 9, 2015 at 16:43
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    $\begingroup$ clearly the mass A would like to follow the direction of the gravitational acceleration...combining this with the equivalence principle might lead you to solve this with just some basic trig... $\endgroup$
    – Phoenix87
    Jan 9, 2015 at 16:44
  • $\begingroup$ @Floris thank you for noticing that i need to dance around $\theta$ not $t$. If you like you can issue your comment as an answer and i will accept. $\endgroup$
    – Yola
    Jan 9, 2015 at 16:48

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I don't think you need to build a full differential equation: draw the forces on the mass and the relationship will follow because it's asking for θ˙(θ) and not θ˙(t). In fact I wonder whether you can't simply rotate the frame of reference until you have a single "acceleration vector" (the combination of $a$ and $g$) pointing straight down, at which point you would be looking at a pendulum with non-small deflection...

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