The motion of a particle in S.H.M. is described by the displacement function, `x=Acos(omegat+phi)`, If the initial `(t=0)` position of the particle is 1cm and its initial velocity is `omega cm s^(-1)`, what are its amplitude and initial phase angle ? The angular frequency of the particle is `pis^(-1)`. If instead of the cosine function, we choose the sine function to describe the SHM`: x=B sin(omegat+alpha)`, what are the amplitude and initial phase of the particle with the above initial conditions ?

Explanation

To solve the problem step by step, we will analyze the two displacement functions given in the question: \( x = A \cos(\omega t + \phi) \) and \( x = B \sin(\omega t + \alpha) \).

### Part 1: Finding Amplitude and Phase for \( x = A \cos(\omega t + \phi) \)

1. **Initial Conditions**:
- At \( t = 0 \), the displacement \( x(0) = 1 \) cm.
- The initial velocity \( v(0) = \omega \) cm/s.
- The angular frequency \( \omega = \pi \) s\(^{-1}\).
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