Question

# The motion of a particle executing simple harmonic motion is described by the displacement function, .  If the initial position of the particle is 1 cm and its initial velocity is  cm/s, 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 , what are the amplitude and initial phase of the particle with the above initial conditions.

Hard
Updated on : 2022-09-05
Solution
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## Intially, at t = 0; Displacement, Intial velocity, Angular frequency,   It is given that,   ...(i)  Velocity,   ...(ii) Squaring and adding equations (i) and (ii), we get: Dividing equation (ii) by equation (i), we get: SHM is given as: Putting the given values in this equation, we get:   ...(iii) Velocity, Substituting the given values, we get:  ...(iv) Squaring and adding equations(iii) and (iv), we get: Dividing equation (iii) by equation (iv), we get: ......

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