    Question

# A particle starts from mean position x=0 and starts moving towards negative extreme position. Find the initial phase constant ϕ of the particle.

A
ϕ=0
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B
ϕ=π2
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C
ϕ=π
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D
ϕ=π4
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Solution

## The correct option is C ϕ=π Since the particle starts at mean position, we know that, the displacement can be written as x=A sin(ωt+ϕ) ……(1) From this by differentiating we get, V=A ω cos(ωt+ϕ) ……(2) Since, particle was initially at x=0, from equation 1 we get, 0=A sin ϕ⇒sin ϕ=0∘⇒ϕ=nπ where n=0,1,2,3..... ϕ can be 0 , π , 2π..... Since the particle is moving towards negative extreme position, at t=0, Particle velocity is negative A ω cos ϕ<0 ⇒cos ϕ<0 If, ϕ=0∘,2π,4π... then cos ϕ>0 But, If ϕ=π,3π,5π.... then cos ϕ<0 So, we can conclude that ϕ=π,3π,5π..... Hence option (c) is the correct answer.  Suggest Corrections  0      Similar questions
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