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Question

Two particles move parallel to x axis about the origin with same amplitude a and frequency ω. At a certain instant they are found at a distance a/3 from the origin on opposite sides but their velocities are in the same direction. What is the phase difference between the two?

A
cos179
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B
cos159
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C
cos149
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D
cos119
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Solution

The correct option is C cos179
Let x1=asinωt and x2=asin(ωt+δ) be two SHMs.
a3=asinωt and a3=asin(ωt+δ)
sinωt=1/3 and sin(ωt+δ)=1/3
sin(ωt+δ)=sinωtcosδ+cosωtsinδ
On puting the valus of sinωt &cosωt
13cosδ+119sinδ=13
9cos2δ+2cosδ7=0
cosδ=1 or 79
i.e, δ=180o or cos1(79)
If we put 180o, we find that v1 and v2 are of opposite signs.
Hence δ=180o is not applicable.
δ=cos1(79)

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