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Sagot :
Answer:
Aₓ = A_y = A
wₓ = w_y = w
Фₓ = Ф_y = Ф
Explanation:
For a movement to be circular it must meet the exception of the circle
R² = x² + y²
in the exercise indicate the expressions of the movement in the two axes
x (t) = Aₓ cos (wₓ t + Фₓ)
y (t) = A_y cos (w_y t + Ф_y)
we substitute
R² = Aₓ² cos² (wₓ t + Фₓ) + A_y² sin² w_y t + Ф_y)
for this expression to be a circle it must meet
Aₓ = A_y = A
wₓ = w_y = w
Фₓ = Ф_y = Ф
with these expressions
R² = A² [cos² (w t + Ф) + sin² (wₓ t + Фₓ) ]
use the trigonometry relationship
cos² θ + sin² θ = 1
R² = A²
Therefore, it is fulfilled that it is a circle whose radius is equal to the amplitude of the movement
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