(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An object is moving along an ellipse which is described by x(t)=acos(^{[tex]\omega[/tex]}t) and y(t)=bsin([tex]\omega[/tex]t). Determine magnitude of acceleration vector as a function of parameters a, b, and [tex]\omega[/tex]. Is magnitude of acceleration vector constant over time?

2. Relevant equations

r(t)=x(t)x+y(t)y

v=dx/dtx+dy/dty

3. The attempt at a solution

r(t)=acos([tex]\omega[/tex]t)x+bsin([tex]\omega[/tex]t)y

a(t)=dvx/dtx+dvy/dty

v=-a[tex]\omega[/tex]sin([tex]\omega[/tex]t)x+b[tex]\omega[/tex]cos([tex]\omega[/tex]t)y

a=-a[tex]\omega[/tex][tex]^{}2[/tex]cos([tex]\omega[/tex]t)x-b[tex]\omega[/tex][tex]^{}2[/tex]sin([tex]\omega[/tex]t)y=-[tex]\omega[/tex][tex]^{}2[/tex](acos([tex]\omega[/tex]t)x+bsin([tex]\omega[/tex]t)y

a=-[tex]\omega[/tex]2r(t)

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# Homework Help: 2-D Acceleration Vector

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