Question

The motion of a particle executing simple harmonic motion is described by the displacement function, x(t) = A cos (ωt+ Ф).If the initial (t = O) position of the particle is 1 cm and its initial velocity is ωcm/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+∝), what are the amplitude and initial phase of the particle with the above initial conditions.

Answer 1

иσнєу тнєяє ιѕ αиѕωєя !!!!
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ι нσρє уσυ нєℓρ !!!
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мαяк мє вяαιи ℓιѕт fяιєи∂ ..... !!!
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иσω,
тнє уσυя qυєѕтισи ιѕ ѕтαят .. ?

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иσт υи∂єяѕтαи∂ѕ ѕσ αѕк мє !!!/
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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:


ѕσℓνє ιт α¢σσ∂ιиg тσ єqυ...