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The instantaneous displacement of a simple harmonic oscillator is given by y = A cos(ωt + π/4). Its speed will be maximum at the time

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in Machine Kinematics by (38.0k points)
The instantaneous displacement of a simple harmonic oscillator is given by y = A cos(ωt + π/4). Its speed will be maximum at the time

(a) 2π/ω

(b) ω/2π

(c) ω/π

(d) π/4ω

This question was posed to me in an international level competition.

I'd like to ask this question from Velocity and Acceleration of a Particle Moving with Simple Harmonic Motion in chapter Simple Harmonic Motion of Machine Kinematics

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by (106k points)
Correct choice is (d) π/4ω

For explanation: The velocity is the time derivative of displacement: v = dy/dt = -Aω(sin ωt + π/4). Its maximum magnitude equal to Aω is obtained when ωt = π/4, from which t = π/4ω.

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