Q. 14.7 The motion of a particle executing simple harmonic motion is described by the displacement function,
If the initial 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.
at t = 0
at t = 0
Squaring and adding equation (i) and (ii) we get
Dividing equation (ii) by (i) we get
at t = 0
at t = 0
Squaring and adding equation (iii) and (iv) we get
Dividing equation (iii) by (iv) we get