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- Homework Statement
- A wagon is moving down a curve with friction. There's a pendulum of length ##l## inside it. Find its period

- Relevant Equations
- Period of a pendulum

I was solving problems about the period of a pendulum inside an elevator. They're all the same. If the elevator accelerates upwards you have that the period is shorter and it's longer if the direction is downwards.

But I tried to solve something more difficult and I thought about a pendulum inside a wagon which is going down a curve (not an inclined plane)

I wanted to find its period, but I don't know how to start. I mean, I wanted to use polar coordinates so that the radial axis is aligned with the string and you have the tension. But what's ##\theta##? Because it changes. How should I decompose the weight?

Then, are there any pseudo-forces? Because I think about centrifugal force since it is moving along a circle. And what about Coriolis? Because the pendulum has a relative velocity

And how does the friction change the situation?

And then which acceleration should I plug in the equation of period??

If you can, please attach an image with your explanation to make it easier to understand what angles and forces I should take into account

But I tried to solve something more difficult and I thought about a pendulum inside a wagon which is going down a curve (not an inclined plane)

I wanted to find its period, but I don't know how to start. I mean, I wanted to use polar coordinates so that the radial axis is aligned with the string and you have the tension. But what's ##\theta##? Because it changes. How should I decompose the weight?

Then, are there any pseudo-forces? Because I think about centrifugal force since it is moving along a circle. And what about Coriolis? Because the pendulum has a relative velocity

And how does the friction change the situation?

And then which acceleration should I plug in the equation of period??

If you can, please attach an image with your explanation to make it easier to understand what angles and forces I should take into account