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Question

For the given situation, which of the following options correctly represents the equation for SHM?


A
x=Asin(ωt+5π6)
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B
x=Asin(ωt+π6)
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C
x=Asin(ωt5π6)
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D
x=Asin(ωtπ6)
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Solution

The correct option is A x=Asin(ωt+5π6)
For a particle executing SHM, we can say that,
x=Asin(ωt+ϕ) ......(1)
From the data given in the figure,
At t=0,x=A2A2=Asinϕ
ϕ=π6 or 5π6

Differentiating (1) with respect to time on both sides, we get
v=Aωcos(ωt+ϕ)
Also, from the diagram, we can deduce that the particle is moving towards the negative extreme position.
Thus, at t=0, velocity of the particle is negative.
v=Aωcosϕ<0cosϕ<0ϕ=5π6
Subitituting ϕ=5π6 in (1), we get
x=Asin(ωt+5π6)
Thus, option (a) is the correct answer.

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