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Asked by nipunverma59 | 31 Mar, 2019, 13:58: PM
answered-by-expert Expert Answer
If we start time t=0 from point A, we write the equation for displacement x as
 
x = A sin(ωt - φ) ...............(1)
 
where A is amplitude of SHM = 15 cm
ω = 2π/T and T is period of SHM = 20 s
φ = (π/2) (12/15)  = 2π/5  and φ is the phase angle at point A.
 
hence eqn.(1) is written as,   x = 15 sin[ (π/10) t - (2π/5) ] .........................(2)
 
if we differntiate eqn.(1), we get,  
 
( dx/dt ) = 15×(π/10) cos[ (π/10) t - (2π/5) ] = (3π/2) cos[ (π/10) t - (2π/5) ]  ................( 3 )
 
eqn.(3) is rewritten as,    dx  = (3π/2) cos[ (π/10) t - (2π/5) ] dt  .............................(4)
 
let τ be the time taken to travel from point A to point B, then we integrate both sides of eqn.(4)
 
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It is possible to calculate time τ from the eqn.(6)
Answered by Thiyagarajan K | 31 Mar, 2019, 17:25: PM

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