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Questions  

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then its periodic time (in seconds) is

a
4π3
b
8π3
c
7π3
d
3π8

detailed solution

Correct option is B

At this time (when x=4 cm) velocity and acceleration have same magnitudeGiven A=5 cm and  at displacement x=4cm, velocity = acceleration ⇒ωA2-x2=−ω2x ⇒52-42=ω(4) ⇒ω=34=2πT ⇒T=8π3

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