Solving a Cycloid Equation: Finding θ(t)

[thomas91]

Yes.So now you can insert this into your solution and solve for theta to get ...?

Sorry but... If I know

and I know B = 0. What I need to get?

 

[Orodruin]

You still need to solve for $\theta(t)$. Your solution was for \cos(\theta)##...

 

[thomas91]

You still need to solve for $\theta(t)$. Your solution was for \cos(\theta)##...

Then...

Is correct? Thanks!

 

[Orodruin]

No, theta is a function of time.

 

[thomas91]

Then... Recapitulating
2nd condition = > θ' = 0 and t = 0 (rest position)
So I obtained B setting θ' (t = 0) = 0; so B = 0

And now, knowing A and B I have the solution for cos(θ/2)

 

[Orodruin]

And now, knowing A and B I have the solution for cos(θ/2)

So theta becomes ...?

 

[thomas91]

Hello!

¿

?

Thanks!

 

[Orodruin]

Hello!

¿

?

Thanks!

There we go!

 

[thomas91]

Finally! How can I calculate the oscillation period of the bean?

 

[Orodruin]

How long does it take until it returns to the original position?

 

[thomas91]

It will be

?

Simplified:

Thanks!

 

[Orodruin]

Bingo!

Or even simpler
$$
T= 4\pi \sqrt{\frac{a}{g}}
$$

 

[thomas91]

Thanks for everything Orodruin! Have a nice day :D