Question

Two collinear harmonic oscillations x1 = 8 sin (100 t) and x2 = 12 sin (96 t) are
superposed. Calculate the values of time when the amplitude of the resultant
oscillation will be (i) maximum and (ii) minimum.

Answer 1

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

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