Relative rotational motion on a disc

[Like Tony Stark]

Homework Statement

$A$ oscillates along the central position $O$ with amplitude $5 cm$ at a frecuency $2 hz$ such that its displacement measured in $cm$ in function of time is governed by $x=5sin(4 \pi t)$, where $t$ is measured in seconds. An angular acceleration around $O$ is applied to the disc with an amplitude $20 rad$ at a frequency $4 hz$ such that $\theta =0.20sin(8 \pi t)$. Determine the acceleration of A for $x=0 cm$ and $x= 5 cm$.

Relevant Equations

$\vec a=\vec a_B + \vec{\dot \omega} X \vec r + \vec \omega X \vec \omega X \vec r + 2. \vec \omega . \vec v_{rel} + \vec a_{rel}$

The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. $\vec a_B=0$ because the origin isn't accelerated, $\vec{\dot \omega} X \vec r$ would be $x=5sin(4 \pi .5)$ (in the second case), and then what numbers should I plug in $\vec \omega X \vec \omega X \vec r$, $2. \vec \omega . \vec v_{rel}$ and $\vec a_{rel}$?
I don't understand relative rotational motion very well. I mean, I just have to plug the data in the formula, but I don't know what's the data that I have.

 

[haruspex]

Homework Statement: $A$ oscillates along the central position $O$ with amplitude $5 cm$ at a frecuency $2 hz$ such that its displacement measured in $cm$ in function of time is governed by $x=5sin(4 \pi t)$, where $t$ is measured in seconds. An angular acceleration around $O$ is applied to the disc with an amplitude $20 rad$ at a frequency $4 hz$ such that $\theta =0.20sin(8 \pi t)$. Determine the acceleration of A for $x=0 cm$ and $x= 5 cm$.
Homework Equations: $\vec a=\vec a_B + \vec{\dot \omega} X \vec r + \vec \omega X \vec \omega X \vec r + 2. \vec \omega . \vec v_{rel} + \vec a_{rel}$

The first doubt that comes to my mind is "I have to determine the acceleration with respect to what?", because the problem doesn't tell. Then, I have some problems when having to plug the data in the formula of acceleration. $\vec a_B=0$ because the origin isn't accelerated, $\vec{\dot \omega} X \vec r$ would be $x=5sin(4 \pi .5)$ (in the second case), and then what numbers should I plug in $\vec \omega X \vec \omega X \vec r$, $2. \vec \omega . \vec v_{rel}$ and $\vec a_{rel}$?
I don't understand relative rotational motion very well. I mean, I just have to plug the data in the formula, but I don't know what's the data that I have.View attachment 249344

There's something wrong with your equation. $2. \vec \omega . \vec v_{rel}$ would be a scalar.
For the cross products, use \times; and the triple cross product needs parentheses.

No equation is meaningful without a statement of the context and definitions of the variables. Please state these for your relevant equation.