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Question

Find out the phase constant ϕ [in rad] of a particle performing SHM, if the initial conditions are as shown in the figure.



Your Answer
A
π3
Your Answer
B
4π3
Correct Answer
C
5π3
Your Answer
D
π6

Solution

The correct option is C 5π3
Let's assume the equation of the particle executing SHM is
x=Asin(ωt+ϕ) ......(1)
From the data given in the diagram, we can say that at t=0,x=3A2
3A2=Asinϕ
ϕ=4π3 or 5π3
Differentiating (1) with respect to time, we get
v=Aωcos(ωt+ϕ)
Also from the figure, we can see that the particle is moving towards positive extreme position.
At t=0,v>0
v=Aωcosϕ>0cosϕ>0ϕ=5π3 rad
Thus, option (c) is the correct answer.

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