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Simple Harmonic Motion question

2011 · Shift 2 · Q44
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  5. /2011 · Shift 2 · Q44

Simple Harmonic Motion question

2011 · Shift 2 · Q44

JEE AdvancedPhysicsSimple Harmonic MotionMCQ+3 / −0.75
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t)=Asin⁡ωt{x_1}\left( t \right) = A\sin \omega tx1​(t)=Asinωt and x2(t)=Asin⁡(ωt+2π3){x_2}\left( t \right) = A\sin \left( {\omega t + {{2\pi } \over 3}} \right)x2​(t)=Asin(ωt+32π​). Adding a third sinusoidal displacement x3(t)=Bsin⁡(ωt+ϕ){x_3}\left( t \right) = B\sin \left( {\omega t + \phi } \right)x3​(t)=Bsin(ωt+ϕ) brings the mass to a complete rest. The values of B and ϕ\phiϕ are
  1. A
    2A,3π4\sqrt 2 A,{{3\pi } \over 4}2​A,43π​
  2. B
    A,4π3A,{{4\pi } \over 3}A,34π​
  3. C
    3A,5π6\sqrt 3 A,{{5\pi } \over 6}3​A,65π​
  4. D
    A,π3A,{\pi \over 3}A,3π​
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