The instantaneous displacement of a simple pendulum oscillator is given by x=Acos (wt+π/4). It's speed will be maximum at time

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Solution

Given Displacement x = Acos (wt+π/4)

The speed of pendulum oscillator will be the time derivative of displacement:

v = dy/dt = -Aωsin (ωt + π/4).

We know sinθ will attain maximum value at θ = π/2

ωt + π/4 = π/2

ωt = π/2 - π/4

ωt = π/4

Its maximum magnitude equal to Aω is obtained when ωt = π/4, from which t = π/4ω

Answer : Time t = π/4ω

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