Answer:
-2π ≤ ∅ ≤ 3π/2
0 ≤ ∅ ≤ π/2
Explanation:
In simple harmonic motion, the displacement and velocity vectors are as follows:
[tex]x(t) = A\cos(\omega t + \phi)\\v(t) = -\omega A\sin(\omega t + \phi)[/tex]
where ∅ is the phase angle. At t = 0, the initial displacement and velocity are
[tex]x(0) = A\cos(\phi)\\v(0) = -\omega A\sin(\phi)[/tex]
According to two equations, we need to find the ∅ values which makes both cosine and sine terms positive.
So, ∅ is in the range: [-2π, -3π/2] and [0,π/2]
