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$\begingroup$ So you're saying that pendulum will never reach equilibrium in this case. Clearly it does , exactly when it reaches angle arctan ( a/g) because net force becomes zero. $\endgroup$– An_ElephantCommented Sep 24, 2023 at 13:16
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$\begingroup$ No, if you have a normal pendulum with equilibrium in the middle, if you push it once it will move all the time it goes to equilibrium only by friction, which you neglected . same with an accelerating car the pendulum goes beyond equilibrium point. when it reaches equilibrium point, you are right, force is zero, but it still has velocity or kinetic energy, like you proved by the way with your calculation. $\endgroup$– trulaCommented Sep 24, 2023 at 14:48
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$\begingroup$ So the pendulum will never be at rest even according to car frame ? But my book question says that to find the angle at which it gets finally hanged at. $\endgroup$– An_ElephantCommented Sep 24, 2023 at 15:04
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$\begingroup$ in reality you have friction in your car, as outside, so after some time you reach equilibrium same with the pendulum you pushed, and then it stays that way, since there is no force. Thats why you have to calculate the point of zero force . $\endgroup$– trulaCommented Sep 24, 2023 at 15:08
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$\begingroup$ Okay thanks. I get it. $\endgroup$– An_ElephantCommented Sep 24, 2023 at 15:11
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