Q. A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin(ωt + π/6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?
A) T/12
B) T/8
C) T/6
D) T/3
Explanation
[Solution from source] v = aω cos(ωt + π/6). Setting v = aω/2 gives ωt + π/6 = π/3, so ωt = π/6 and t = (π/6)(T/2π) = T/12. T/6 would be the answer if the initial phase π/6 were ignored. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.