Is acceleration magnitude constant for an object moving along an ellipse?

[eestep]

Homework Statement

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

Homework Equations

r(t)=x(t)x+y(t)y
v=dx/dtx+dy/dty

The Attempt at a Solution

r(t)=acos($$\omega$$t)x+bsin($$\omega$$t)y
a(t)=dvx/dtx+dvy/dty
v=-a$$\omega$$sin($$\omega$$t)x+b$$\omega$$cos($$\omega$$t)y
a=-a$$\omega$$$$^{}2$$cos($$\omega$$t)x-b$$\omega$$$$^{}2$$sin($$\omega$$t)y=-$$\omega$$$$^{}2$$(acos($$\omega$$t)x+bsin($$\omega$$t)y
a=-$$\omega$$2r(t)

 

[ehild]

I assume that you mean the unit vectors along the axes x,y by "x" and "y" and both "r" and "a" are vectors. Your last equation is the relation between the vector of acceleration and the position vector. What is the magnitude of acceleration?

ehild

 

[eestep]

Am I approaching it incorrectly? Both "r" and "a" are vectors. I assume I have to find magnitude of vector "r" but am not certain how to do it.

 

[ehild]

Do you know how to calculate the magnitude of a vector from its components?

ehild

 

[eestep]

I believe I calculate it by doing the square root of its components squared. Is that right?