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

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(1) (8π)/3. In SI units v=ω√A²-x²=ω√0.05²-0.04²=0.03ω and |a|=ω²x=0.04ω². Setting them equal: 0.03ω=0.04ω², so ω=0.75 rad s⁻¹. T=(2π)/(0.75)=(8π)/3 s.

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

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