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Can any one help me with the following.

A simple pendulum is suspended from the ceiling of a lift. It is moving upward with acceleration $a$. The string of the effective length of the pendulum makes angle $\alpha$ with the vertical. Choose the point of suspension as origin, $x$-axis along the horizontal and $y$-axis vertically downwards. Express $x$ and $y$ in terms of plane polar coordinates at time $t$ after the lift takes off

Now I understand it will be

$x = l \sin\alpha$ and $y = l \cos\alpha$ where $l$ is the length of the pendulum string

but it seems correct answer is $y = l \cos\alpha - \frac{1}{2}at^2$

can any one please explain why and how the other factor is included in the equation and why it is not affecting the $x$ and affecting only $y$

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closed as off-topic by Brandon Enright, Jim, John Rennie, jinawee, Valter Moretti Apr 17 '14 at 18:27

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The origin is assumed to be at rest wrt ground frame. So, your pendulum with lift moves up and the origin stays at its original place only. That explains that factor.

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  • $\begingroup$ Yeah, in that case it make sense :) $\endgroup$ – AVS Apr 16 '14 at 9:47

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