# Path/time function of a freesbie (the ride at amusement parks)

Kakainsu
You don't seem to have understood my post #27.
You need to write the unit vectors as functions of time, using the knowledge that the pendulum will be executing SHM. Then you can differentiate wrt time.
How can I write unit vectors as functions of time?

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How can I write unit vectors as functions of time?
You have (x , y) vectors for them in terms of ##\phi##, and you can get ##\phi## as a function of t from the SHM equation.

Kakainsu
You have (x , y) vectors for them in terms of ##\phi##, and you can get ##\phi## as a function of t from the SHM equation.

So phi = w*t?

But how can I go on from there? I mean i don't know how to differentiate this...can you maybe give me an example of how you would differntiate the circular motion with changing planes, so expressed by e_phi and e_s? I'd be super happy, I really want to understand it but its hard

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So phi = w*t?
No, it is a pendulum. For small swings, it will be something like ##\phi=\phi_{max}\sin(\omega_p t)##. To get ##\dot\phi##, just differentiate that.
Note that ##\omega_p## is unrelated to the ##\omega## we introduced for the uniform rotation of the Frisbee about its axis.

Kakainsu
No, it is a pendulum. For small swings, it will be something like ##\phi=\phi_{max}\sin(\omega_p t)##. To get ##\dot\phi##, just differentiate that.
Note that ##\omega_p## is unrelated to the ##\omega## we introduced for the uniform rotation of the Frisbee about its axis.

Could you please be so kind and differentiate the path/time function twice? I know it's a lot but I just don't get it.

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Could you please be so kind and differentiate the path/time function twice? I know it's a lot but I just don't get it.
First, we have to get that function in terms of t and constants. I have given you the general form of the function for the pendulum angle. From that, obtain the function for the position of the Frisbee's centre.
Post what you get.