Grade 12th passMechanics

Two collinear harmonic oscillations 8sin (100 ) 1 x = πt and 12sin (96 ) 2 x = πt are superposed. Calculate the (i) maximum and minimum amplitudes, and (ii) the frequency of amplitude modulation.

shakti

7 Years agoGrade 12th pass

1 Answer

Arun

7 Years ago

When 2 harmonic oscillations x₁ and x₂ are superimposed then the resultant is given as X= x₁ + x₂

if x₁= a₁sin(ωt+Ф₁) ,x₂=a₂sin(ωt+Ф₂)
⇒ X= Asin(ωt+Ф)
Ф= Ф₁-Ф₂ is called phase difference
in above question Ф= 100t-96t=4t

(i) the amplitude of resultant oscillation is maximum when Ф= 360°
4t= 360
⇒ t=90s
(ii) the amplitude of resultant oscillation is minimum when Ф= 180°
4t= 180
⇒ t= 45s

Regards

Arun (askIITians forum expert)

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Two collinear harmonic oscillations 8sin (100 ) 1 x = πt and 12sin (96 ) 2 x = πt are superposed. Calculate the (i) maximum and minimum amplitudes, and (ii) the frequency of amplitude modulation.

shakti

1 Answer

Arun

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