The motion of a particle executing simple harmonic motion is described by the displacement function, x (t) = A cos (ωt + φ).If the initial (t = 0) position of the particle is 1 cm and its initial velocity is ω cm/s, what are its amplitude and initial phase angle? The angular frequency of the particle is π s–1. If instead of the cosine function, we choose the sine function to describe the SHM: x = B sin (ωt + α), what are the amplitude and initial phase of the particle with the above initial conditions.

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Initially, at t = 0: Displacement, x = 1 cm Initial velocity, v = ω cm/sec. Angular frequency, ω = π rad/s–1 It is given that: 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...
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Initially, at t = 0: Displacement, x = 1 cm Initial velocity, v = ω cm/sec. Angular frequency, ω = π rad/s–1 It is given that: 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: Velocity, Substituting the given values, we get: Squaring and adding equations (iii) and (iv), we get: Dividing equation (iii) by equation (iv), we get: read less
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