The correct option (D) – (√3/32)π2
Explanation:
y = Asinωt
V = (dy/at) = Aωcosωt
a = (dv/dt) = – Aω2 sin ωt
from graph, A = 1cm
T = 8sec
∴ ω = (2π/T) = (2π/8) = (π/4)
t = (4/3)
hence a = (– 1) (π/4)2 sin {(π/4) × (4/3)}
∴ a = – (π/4)2 × sin (π/3)
= – (√3/2) × (π2/16)
= – (√3/32)π2