soln

Asked by as9875147324 | 5th May, 2022, 05:24: 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 )

Answered by Thiyagarajan K | 5th May, 2022, 08:38: PM

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