A particle executes a simple harmonic motion of time period T. Findthe time taken by the particle to have a displacement from meanposition equal to one half of the amplitude.
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Let amplitude of SHM = A₀
A = A₀ sin(ωt)
where A = displacement
t = time
ω = angular frequency = 2π/T
given that A = A₀/2
A₀/2 = A₀ sin(ωt)
⇒ 1/2 = sin(ωt)
⇒ 1/2 = sin(2π/T × t)
⇒ 2π/T × t = sin⁻¹(1/2) = π/6
⇒ t = π/6 × T/2π
⇒ t = T/12
A = A₀ sin(ωt)
where A = displacement
t = time
ω = angular frequency = 2π/T
given that A = A₀/2
A₀/2 = A₀ sin(ωt)
⇒ 1/2 = sin(ωt)
⇒ 1/2 = sin(2π/T × t)
⇒ 2π/T × t = sin⁻¹(1/2) = π/6
⇒ t = π/6 × T/2π
⇒ t = T/12
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