Question

What is the value of the phase angle ϕ if the initial velocity is positive and the initial displacement is negative?

Answer 1

The value of the phase angle ϕ in this case depends on the specific context of the problem. However, in general, if the initial velocity is positive and the initial displacement is negative, the phase angle ϕ can be considered to be negative.

Step-by-step explanation:

The value of the phase angle ϕ in this case depends on the specific context of the problem. However, in general, if the initial velocity is positive and the initial displacement is negative, the phase angle ϕ can be considered to be negative.

1. Since the underlying speed is positive, it implies the article is moving in the positive bearing.

2. Then again, the underlying dislodging is negative, demonstrating that the item begins its movement from a situation the other way of the positive pivot.

3. Taking into account these circumstances, the stage point ϕ will be π radians, or 180 degrees.

In this way, the worth of the stage point ϕ, when the underlying speed is positive and the underlying dislodging is negative, is:

ϕ = π radians or 180 degrees.

Answer 2

-2π ≤ ∅ ≤ 3π/2

0 ≤ ∅ ≤ π/2

Step-by-step explanation:

In simple harmonic motion, the displacement and velocity vectors are as follows:

`x(t) = A\cos(\omega t + \phi)\\v(t) = -\omega A\sin(\omega t + \phi)`

where ∅ is the phase angle. At t = 0, the initial displacement and velocity are

`x(0) = A\cos(\phi)\\v(0) = -\omega A\sin(\phi)`

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]