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## Homework Statement

An object with mass m undergoes simple harmonic motion, following 2 perpendicular directions, described by the equations:

x=a cos (wt), a>0,

y=b cos (2wt), b>0

a) find the equation of the trajectory

b) find the speed at any given time (so having t as a variable)

c) the maximum force F which acts on the object at any given time (again, having t as a variable).

## Homework Equations

## The Attempt at a Solution

So far: a) from x=a cos (wt) we get cos (wt)=x/a; in the y equation, we can expand as follows:

cos (2wt)=cos^2 (wt) - sin^2 (wt). We also know that for any real x we have cos^2 (x) +sin^2(x)=1, therefore cos (2wt)=cos^2 (wt) - sin^2 (wt)=cos^2 (wt) + cos^2(wt)-1; therefore y=b (2cos^2 (wt) -1 )=b( x^2/a^2 -1 ), which is the equation of the trajectory.

Now for b) and c), I'm not quite sure how to use what I have. I differentiated the x and y equation from the beginning, differentiated the trajectory and somehow I need to combine them. I suppose the idea from b) applies to c).

I would be grateful if you could give me some hints :)

Have a great day,

Adrian

PS: If it is not clear, I could rewrite using latex.