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soln
Asked by as9875147324 | 05 May, 2022, 17:24: PM
Expert Answer
Let us consider equation of displacement x of SHM is
x = A sin (ω t + φ ).................. (1)
where A is amplitude , ω is angular frequency and φ is initial phase constant
we are given that at time t = T/2 , displacement x = A/2 , where T is period of SHM
Equation (1) is written at time t = T/2 as
A/2 = A sin [ ω( T/2 )+ φ ] = A sin ( π/2 + φ )
i.e ( π/2 + φ ) = sin-1 (1/2)
RHS of above expression can be π/6 or 5π/6
If ( π/2 + φ ) = π/6 , then φ is negative but that is not given in list of options
If ( π/2 + φ ) = 5π/6 , then φ = π/3
hence we get equation of displacement x of SHM as
x = A sin (ω t + π/3 )
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