The motion of a particle executing simple harmonic motion is described by the displacement function, If the initial (t ) position of the particle is and its initial velocity is , what are its amplitude and initial phase angle? The angular frequency of the particle is . If instead of the cosine function, we choose the sine function to describe the SHM: , what are the amplitude and initial phase of the particle with the above initial conditions. Solution:
The motion of a particle executing simple harmonic motion is described by the displacement function, If the initial (t ) position of the particle is and its initial velocity is , what are its amplitude and initial phase angle? The angular frequency of the particle is . If instead of the cosine function, we choose the sine function to describe the SHM: , what are the amplitude and initial phase of the particle with the above initial conditions. Solution:

At positlon, t = 0,

The given function is  Differentiating equation (1) with respect to t, we get,

Velocity,  On Squaring and adding equations (2) and (4), we get, Dividing equation (4) by equation (2),   Squaring and adding equations(5) and (6), we get: Dividing equation (5) by equation (6), we get:  As a result, 