Answer:
the orbit resulting an ELIPSE
Explanation:
Harmonic motion is described by the expression
x = A cos (wt +Ф₁)
In this exercise it is established that in the y axis there is also a harmonic movement with the same frequency, so its equation is
y = B cos (wt + Ф₂)
the combined motion of the two bodies can be found using the Pythagorean theorem
R² = x² + y²
R² = [A² cos² (wt + Ф₁) + B² cos² (wt + Ф₂)]
to simplify we can assume that the phase in the two movements are equal
R = √(A² + B²) cos (wt + Ф)
If the two amplitudes are equal we have a circular motion, if the two amplitudes are different in elliptical motion, the amplitudes of the two motions are
circular R² = (A² + A²)
elliptical R² = (A² + B²)
We see from the last expression that the broadly the two axes is different, so the amplitude is an ellipse.
By which the orbit resulting an ELIPSE
