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The displacement of a particle performing linear harmonic motion starting from mean position in half of
time period is
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The amplitude at the extremes are +A and -A respectively. Comparing x=6sin(3πt+5π/6) with x=Asin(ωt+ϕ), we get amplitude A = 6.
For the particle to reach the amplitude, we have (3πt−5π/6)=π/2⟹3πt=5π/6+3π/6=4π/3
Thus, t = 4/9 secs
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t=4/9 hope it helps you
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