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December 11th, 2016, 03:43 PM   #11
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Yes, I wound up doing a number of edits. Sorry for the confusion.

By "vertical" I presume you mean when the pendulum is at its lowest level (ie. the string is straight up and down)? That would correspond to $\displaystyle \theta = 0$. So let $\displaystyle \theta (t) = 0$ and solve for t.

Max height is the largest value of $\displaystyle \theta$. So you are finding the (absolute) maximum of $\displaystyle \theta$, which we know to be $\displaystyle \theta _0$. Find the first derivative and set it equal to 0, then solve for t.

-Dan
Thank you very much for your help dan, if you could just solve for vertical 1st time t, that would completely satisfy everything i wanted to know, thank you very much
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December 11th, 2016, 05:33 PM   #12
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Thank you very much for your help dan, if you could just solve for vertical 1st time t, that would completely satisfy everything i wanted to know, thank you very much
I dont know the last part about vertical height ahaha. could you show me?
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December 11th, 2016, 05:34 PM   #13
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Given
$\displaystyle \theta (t) = A~cos( \omega t) + B~sin( \omega t)$

From the initial condition we have $\displaystyle \theta (t = 0) = \theta _0$

$\displaystyle \theta _0$ is just a constant which defines what $\displaystyle \theta$ is at t = 0. So in the general solution we have:

$\displaystyle \theta (t = 0) = A~cos( \omega \cdot 0) + B~sin( \omega \cdot 0)$

$\displaystyle \theta (t = 0) = \theta _ 0 = A~cos( \omega \cdot 0) + B~sin( \omega \cdot 0)$

$\displaystyle \theta _ 0 = A \cdot 1 + B \cdot 0$

$\displaystyle \theta _ 0 = A$

-Dan
Could you show me time to reach vertical?
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December 11th, 2016, 05:50 PM   #14
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Could you show me time to reach vertical?
When the pendulum is vertical we have $\displaystyle \theta = 0$.

So
$\displaystyle \theta (t) = \theta _0 ~ cos \left ( \sqrt{ \frac{g}{L} }~ t \right ) = 0$

Solve this for t. Divide both sides by $\displaystyle \theta _0$ then take the inverse cosine. (Hint: For what angle is cos(angle) = 0?)

-Dan
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December 11th, 2016, 05:56 PM   #15
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When the pendulum is vertical we have $\displaystyle \theta = 0$.

So
$\displaystyle \theta (t) = \theta _0 ~ cos \left ( \sqrt{ \frac{g}{L} }~ t \right ) = 0$

Solve this for t. Divide both sides by $\displaystyle \theta _0$ then take the inverse cosine. (Hint: For what angle is cos(angle) = 0?)

-Dan
oh yes i did that earlier yes the angle is 90 degrees which means that root gravity over length by time is 90 degrees, but i still have unknowns
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December 11th, 2016, 06:41 PM   #16
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oh yes i did that earlier yes the angle is 90 degrees which means that root gravity over length by time is 90 degrees, but i still have unknowns
What unknowns? It's a single variable equation!

$\displaystyle \theta (t = 0) = 0 = \theta _0 ~ cos \left ( \sqrt{\frac{g}{L}} ~ t \right )$

Dividing both sides by $\displaystyle \theta _0$:
$\displaystyle cos \left ( \sqrt{\frac{g}{L}} ~ t \right ) = 0$

Take the inverse cosine, noting that we are betwen 0 and $\displaystyle \pi$ radians:
$\displaystyle \sqrt{\frac{g}{L}}~t = \frac{\pi}{2}$ (I'll stick with angles in radians as that is the usual convention so make sure to convert to degrees if you have to.)

$\displaystyle \frac{g}{L} t^2 = \frac{\pi ^2}{4}$

$\displaystyle t^2 = \frac{\pi ^2 L}{4g}$

$\displaystyle t = \sqrt{\frac{\pi ^2 L}{4g}} = \frac{\pi}{2} \sqrt{\frac{L}{g}}$


-Dan

Last edited by topsquark; December 11th, 2016 at 06:44 PM.
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