Question

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

A
π3
B
4π3
C
5π3
D
π6

Solution

## The correct option is C 5π3Let'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>0⇒cosϕ>0⇒ϕ=5π3 rad Thus, option (c) is the correct answer.

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